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A research paper is when you research a topic and write about it. Here are some suggestions on how to write a research paper in 10 steps:1. Choose a topic2. Choose a research question3. Create a thesis statement4. Research your topic5. Evaluate your sources6. Take notes on sources7. Create an outline8. Write a draft9. Edit the draft10. Finalize your paper1. CHOOSE A TOPICThe first thing you need to do is to choose a paper topic. Maybe you have been assigned a certain topic already--then you can skip this section. But if you need to come up with your own topic, then choose something that interests you. It’s a lot easier to write a research paper on something that is interesting--otherwise it will be boring and you won’t have a lot of motivation to write a good paper.If you need help choosing a topic, then try these ideas:Go to a university library and visit the section where the books in your subject are located. For example, if you are in an Anthropology class, go to the section of the library where the Anthropology-related books are. (If you need help finding the right section, just ask the librarian.) Browse the books for a couple of hours, and see if you find anything interesting.Browse through an introductory textbook on your subject. Typically, each chapter in an introductory textbook is about a different topic—for example, in an Anthropology textbook, there’ll probably be a chapter on economics, a chapter on gender, a chapter on families and kinship, and so on. See if a certain topic interests you.At your university library, browse through a specialized encyclopedia about your subject. For example, if you are in an Anthropology class, then browse through an Anthropology-related encyclopedia. (Ask your librarian where to find a specialized encyclopedia on your subject.) See if any of the topics in the encyclopedia are interesting.Browse the Oxford Bibliographies website for ideas (you can browse by subject). Go to this website: Oxford Bibliographies - Your Best Research Starts Here - obo (Oxford Bibliographies - Your Best Research Starts Here - obo)2. CHOOSE A RESEARCH QUESTIONNow that you have determined a topic to write about, you need to figure out what aspect of the topic you want to focus on. For example, say you want to research influenza. Are you interested in influenza in a certain country? A certain city? Are you considering all ages or just children? Or maybe the elderly? And what specifically about influenza are you interested in— how people decide to go to the doctor for treatment, or how people avoid the flu, if people get their flu shot, or what? There are so many things that fall under the topic of influenza. You need to narrow the topic down even further.One way to narrow down a topic is to consider it from different angles. For example, you can narrow a topic chronologically (by time) or geographically (by place). Using our influenza example, you could narrow it to a certain time frame, like the last flu season. Or you could narrow the topic by place, and only look at influenza in a certain city or country. Try to narrow down your topic into a more specific one.Once you have narrowed your topic down, write what you want to find out about your topic in the form of a question. This is your research question.You need to make sure that your research question is not too big or too narrow. An example of a research question that is too big is: "What can we do to decrease the number of influenza infections around the world?" There is way too much involved in this question for a small research paper.An example of a research question that is too small is: "How many people were infected with influenza in Seattle, Washington (USA) during the last flu season?" This question is easily answered by a simple number, so you can’t write a whole paper about it.Here are some examples of common types of research questions (taken directly from Developing Strong Research Questions | Criteria and Examples (Developing Strong Research Questions | Criteria and Examples):What are the characteristics of X?What are the similarities between X and Y?What is the relationship between X and Y?What are the main factors in X?What is the role of Y in Z?Does X have an effect on Y?What is the impact of Y on Z?What are the causes of X?What are the advantages and disadvantages of X?How well does Y work?How effective is Z?How can X be achieved?What are the most effective strategies to improve Y?3. CREATE A THESIS STATEMENTIn college, you shouldn’t just be summarizing what you read for a research paper (unless that’s the instructions that your professor gave you). You need to make some kind of point, backed up by your research. The main point of your research paper is called the thesis statement. It is the answer to your research question. A thesis statement should be one or two sentences long.For more information on writing thesis statements, check out the University of Illinois at Urbana-Champaign’s website: Writers Workshop: Writer Resources (Writers Workshop: Writer Resources) and Indiana University at Bloomington’s website: How to Write a Thesis Statement (How to Write a Thesis Statement).Also, try Ashford University’s Thesis Generator at this website: Thesis Generator (Thesis Generator)4. RESEARCH YOUR TOPICNow that you know what your paper is going to be about, you can start researching your topic.The first thing to do is to make a list of keywords relating to your research topic. Think about everything that you know about your topic and come up with a list of keywords to use in researching. For example, say you are doing a project on influenza. You may want to search for the term “flu” along with the medical term “influenza.” For each word on your list of keywords, try to come up with another word that means the same thing (a synonym) and add that to your list of keywords. For example, if one of your keywords is "flu shot,” make sure you also add “influenza vaccine,” because these are different words that mean the same thing.The next thing to do is take your list of keywords and start doing some library research. You need to be looking for journal articles that match your research topic. You’ll need access to a database of journal articles—ask your librarian if you don’t know how to find these kinds of databases in your library. Some examples of article databases are JSTOR and ProQuest, but there are many, many more! Then, start putting your keywords into the database’s search engine and see what you find.But don’t stop there—for each journal article that you find, also check the list of references at the end. The reference list contains the titles of sources that the article’s author used in doing their own background research.So, browse through the list and look for anything that might be related to your own research, and then look up those articles, too. And then check the list of references in THOSE articles for anything that is related to your own research as well. And look up those articles, and so on and so on.Besides searching academic databases, you can also search the internet for information. For example, you can use your keywords to search in Google Scholar, which will bring up reputable sources of information. Just go to Google Scholar (Google Scholar). Another great place to find research articles is ERIC, which stands for Education Resources Information Center. Here is their website: Education Resources Information Center (Education Resources Information Center).In addition, you will want to look for books about your topic. Books may be listed in the reference section of your journal articles. You can also find some by searching your university library’s catalog. You can search the internet, too. A great website to search for books is WorldCat: The World's Largest Library Catalog (The World's Largest Library Catalog)Also, check specialized encyclopedias for information. Many times, there is a list of references after each entry in the encyclopedia. These sources may be helpful for your paper. For example, you can visit the Oxford Bibliographies website I mentioned earlier, at this website: Oxford Bibliographies - Your Best Research Starts Here - obo (Oxford Bibliographies - Your Best Research Starts Here - obo)As you look at the articles and books you find, you will probably come up with more keywords to search for. Just add them to your list and keep researching!You’re going to want to have a good system for keeping track of which keywords you have already searched for, and which databases you have already used, which articles and books you have already read, and which articles you have already checked the list of references.It's easy to start losing track of things, so I suggest using a notebook or Word document and making a sort of diary, just briefly listing things you did such as “I searched the ABC database using keyword #1,” “I searched the XYZ database for keyword #3,” etc. And make some sort of list of which articles and books are read, and which still need to be read, and a list of things to do, and so forth to stay organized.5. EVALUATE YOUR SOURCESJust because you found a source of information doesn’t mean that you should automatically include it in your paper. You need to evaluate each source. Here are a few things to look for:First, check to see if the source is actually relevant for your research paper. You might have found a great source, but it may not really provide much information on your specific research topic.If it is relevant, then check the author of the source to see if they are credible. For example, if the source is a peer-reviewed journal article written by someone with a Ph.D. in their field, then that is most likely a trustworthy source. A blog post written by a non-expert might not be a trustworthy source.Check the publication date to make sure that it’s fairly recent. If you are not sure if a source is too old to use, just ask your professor for guidance.Skim the article and determine if the information is fact or opinion. Consider if the information seems well-researched, or if there is simply information without evidence to support it.For more things to look for, check out the University of Southern California’s website: Research Guides: Organizing Your Social Sciences Research Paper: Evaluating Sources (Research Guides: Organizing Your Social Sciences Research Paper: Evaluating Sources)For some great checklists for evaluating sources, check out these websites:Benedictine University: Research Guides: Evaluating Sources: The CRAAP Test (Research Guides: Evaluating Sources: The CRAAP Test)MLA Style Center: https://style.mla.org/app/uploads/sites/3/2018/09/Checklist-for-Evaluating-Sources.pdf (https://style.mla.org/app/uploads/sites/3/2018/09/Checklist-for-Evaluating-Sources.pdf)Excelsior Online Writing Lab: Evaluation Checklist - Excelsior College OWL (Evaluation Checklist - Excelsior College OWL)6. TAKE NOTES ON SOURCESNow that you have found a bunch of sources, you need to read each one and take notes. You’ll want to have a system of recording notes from each source of information. Sometimes these notes are called "source cards" because they used to be written on 3 by 5 index cards. You can use index cards, or a notebook, or a Word document, or a spreadsheet, or a database document—whatever works for you. If you want to use a database, check out Airtable, which is a free database that you can download onto your computer. (see Airtable’s website at: Airtable: Organize anything you can imagine (Airtable: Organize anything you can imagine))Use one index card or one Word page or one database file for each source. List all the bibliographic information for each source on the card or file. For example, if it is a journal article, list the author, article title, journal name, journal issue & page numbers, publication date, URL (if it has one), the date you accessed the URL, and where you found the article (which library, database, etc.)Here’s an example of what it would look like if you used an index card. You can see how all the bibliographic information is noted on the card.Here’s an example of what the database could look like using Airtable.It's a good idea to put a unique code number on each card or file, so you can refer to the article quickly and easily. I like to use a code number made out of the author’s last name, the date of the article, and the title. I use the first 3 letters of the last name, then the 4 digit date, and then the first 3 letters of the article title. So, in this example article below, the code is KOE2014INF. That way, I can group all the papers under the same author together if I need to. Some people like to just number the cards or files consecutively, and that’s fine, just find a system that works for you.Then, it’s time to start taking notes on each source. Use either a new index card or a new page of your notebook or new Word document and assign that card or file a topic. Then, take notes on your first source, using a new card or file for each different topic, and adding the code on the card or file so that you know which source the info came from. Here’s an example using our made-up influenza research project. You could have a notecard with the topic "history of influenza” on the top of it, and all the notes about the history of influenza on it from source #1: (Please note that this card contains made-up information as an example.)And then you could have a notecard with the topic “transmission of influenza” on it, and then all the notes about the transmission of influenza from source #1 on it. (Please note that this card contains made-up information as an example.)After you are finished taking notes on source #1, repeat the process with source #2. Make a series of notecards or files with different topics, each with notes from source #2. Then continue repeating the process for the rest of your sources.Another way to take notes on each article is to summarize the article in your own words in a one-page grid. That way you have all the information about an article on just one page. I created a template that you can use for this purpose--an image is below, and you can download it for free from my website: Anthropology Digital Products ~ FREE Downloadables (Anthropology Digital Products ~ FREE Downloadables)7. CREATE AN OUTLINENow that you have read and taken notes on all of your sources of information, it is time to create an outline.First, read through all of your notes, and create a list of all the ideas that you want to put in your paper. Then, put the ideas into categories. You can write the ideas down on notecards and physically group them in different categories. Or, you can open a new Word document file, create category headings, and cut and paste items from your list into the file. So, now you should have a bunch of categories with details (items from the list of ideas) under each.You can also try organizing all your information into a concept map (also known as a mind map). Just google “free mind mapping software” if you don’t already have an app for that. Put main ideas in separate “bubbles" and connect them to “bubbles” containing each supporting point. Below is an example of a mind map, showing the 4 fields of Anthropology, and some of the subfields within each field.Using the groups of notecards, Word file with categories and details, and/or the mind map, create an outline. Your first section of the outline should be the introduction, and the last section should be the conclusion. In the middle is the body of the paper. This is where you will list your main points (the categories). Then, under each main point, list your supporting points (the ideas in each category).Here’s an example of an outline based on the mind map above:1. Introduction1. Interesting opening2. Thesis statement2. Cultural Anthropology1. Legal Anthropology2. Business Anthropology3. Environmental Anthropology4. etc.3. Physical Anthropology1. Osteology2. Paleopathology3. Forensic Anthropology4. etc.4. Archaeology1. Geoarchaeology2. Underwater Archaeology3. Experimental Archaeology4. etc.5. Linguistic Anthropology1. Descriptive Linguistics2. Ethnolinguistics3. Sociolinguistics4. etc.6. Conclusion1. Summary2. Thesis StatementFor more information on creating an outline, check out this website: How to Create a Structured Research Paper Outline (with example) (How to Create a Structured Research Paper Outline (with example))8. WRITE A DRAFTWrite a first draft, based on your outline. Don’t worry too much about making everything perfect--it's just a rough draft.As I mentioned previously, your paper should have an introduction, a body, and a conclusion.In the introduction, you introduce the topic you are researching, in a paragraph or two. Try to get your reader’s attention in the introduction. Some ways to do this are by providing a quotation, anecdote, interesting fact, or surprising statistic. Also, explain any background information the reader needs to know. Then, introduce your main point--your thesis statement-- which is usually placed at the end of the introductory paragraph.In the body, you explain or prove your thesis statement. This part will be several paragraphs long. Each supporting point you make should have its own paragraph, where you expand on the point and give evidence or examples.For each supporting point you make, you should have a few sources to back up what you are saying. Make sure that you are giving your sources credit for their ideas. You need to cite your sources in the text of the paper, not just in a bibliography page at the end. Use whatever citation style your professor or discipline requires. Check out the Purdue Online Writing Lab for information on different styles: (Research and Citation Resources // Purdue Writing Lab)It’s also a good idea to put in a few direct quotes to help illustrate your points as well--just be sure to cite the sources correctly. Check out this website for more information on using quotes: Working with Quotations (Working with Quotations)Also, make sure to link one paragraph to the next with transition words, such as “also," "in addition," “however," "as a result,” “finally," etc.In the conclusion, you summarize everything and restate your thesis statement, all in about one paragraph. You can also explain why your thesis statement matters, and/or what the bigger implications are.On the final page(s) is the references (or bibliography). This is where you list all the sources that you used in the paper. Follow your instructor’s requirements for this section of the paper--they may want the references in APA style, MLA style, Chicago style, or something else.When the first draft is finished, take a break and do something else for a while. This break can be a few hours or a day or two or longer--everyone does something different. Then, you can go back to your draft and look at it again through fresh eyes, and revise it.9. EDIT THE DRAFTRead through your paper and ask yourself if everything makes sense. Check to see if the flow of one paragraph to the next is logical. Consider if your main point is well supported by your supporting points. Try reading your paper out loud to see how it sounds.Look carefully for errors in spelling or punctuation. It’s also a good idea to run your draft through a grammar check, too--try Grammarly’s free version: (Write your best with Grammarly.)Double-check that all sources have been cited appropriately in the text (otherwise, you may be accused of plagiarism!). Also, double-check your list of references for errors as well.10. FINALIZE YOUR PAPERAfter you have made all the edits to your paper, once again take a break. After your break, take yet another look at your paper. Read it over again, looking for any last-minute errors, writing that doesn’t make sense, etc. Read it out loud again as well, to make sure everything flows as you want it to. Make any last-minute edits. Then, your paper is finished!Make sure to create a backup copy of your paper, and email a copy to yourself as well. That way, if anything happens to your original copy, you have a backup. Or, if you forget to take your printed-out paper to class, you can print another copy at the last minute on campus with the copy in your email. Turn in your assignment and congratulate yourself on completing the research paper!

noThe expansion of the universe is the increase of the distance between two distant parts of the universe with time.[1]It is an intrinsic expansion whereby the scale of space itself changes. The universe does not expand "into" anything and does not require space to exist "outside" it. Technically, neither space nor objects in space move. Instead it is the metricgoverning the size and geometry of spacetime itself that changes in scale. Although light and objects within spacetime cannot travel faster than the speed of light, this limitation does not restrict the metric itself. To an observer it appears that space is expanding and all but the nearest galaxies are receding into the distance.During the inflationary epoch about 10−32of a second after the Big Bang, the universe suddenly expanded, and its volume increased by a factor of at least 1078(an expansion of distance by a factor of at least 1026in each of the three dimensions), equivalent to expanding an object 1 nanometer (10−9m, about half the width of a molecule of DNA) in length to one approximately 10.6 light years (about 1017m or 62 trillion miles) long. A much slower and gradual expansion of space continued after this, until at around 9.8 billion years after the Big Bang (4 billion years ago) it began to gradually expand more quickly, and is still doing so today.The metric expansion of space is of a kind completely different from the expansions and explosions seen in daily life. It also seems to be a property of the universe as a whole rather than a phenomenon that applies just to one part of the universe or can be observed from "outside" it.Metric expansion is a key feature of Big Bang cosmology, is modeled mathematically with the Friedmann-Lemaître-Robertson-Walker metric and is a generic property of the universe we inhabit. However, the model is valid only on large scales (roughly the scale of galaxy clusters and above), because gravitational attraction binds matter together strongly enough that metric expansion cannot be observed at this time, on a smaller scale. As such, the only galaxies receding from one another as a result of metric expansion are those separated by cosmologically relevant scales larger than the length scales associated with the gravitational collapse that are possible in the age of the universe given the matter density and average expansion rate.Physicists have postulated the existence of dark energy, appearing as a cosmological constant in the simplest gravitational models as a way to explain the acceleration. According to the simplest extrapolation of the currently-favored cosmological model, the Lambda-CDM model, this acceleration becomes more dominant into the future. In June 2016, NASA and ESA scientists reported that the universe was found to be expanding 5% to 9% faster than thought earlier, based on studies using the Hubble Space Telescope.[2]While special relativity prohibits objects from moving faster than light with respect to a local reference frame where spacetime can be treated as flat and unchanging, it does not apply to situations where spacetime curvature or evolution in time become important. These situations are described by general relativity, which allows the separation between two distant objects to increase faster than the speed of light, although the definition of "separation" is different from that used in an inertial frame. This can be seen when observing distant galaxies more than the Hubble radius away from us (approximately 4.5 gigaparsecs or 14.7 billion light-years); these galaxies have a recession speed that is faster than the speed of light. Light that is emitted today from galaxies beyond the cosmological event horizon, about 5 gigaparsecs or 16 billion light-years, will never reach us, although we can still see the light that these galaxies emitted in the past. Because of the high rate of expansion, it is also possible for a distance between two objects to be greater than the value calculated by multiplying the speed of light by the age of the universe. These details are a frequent source of confusion among amateurs and even professional physicists.[3]Due to the non-intuitive nature of the subject and what has been described by some as "careless" choices of wording, certain descriptions of the metric expansion of space and the misconceptions to which such descriptions can lead are an ongoing subject of discussion within education and communication of scientificIn 1929, Edwin Hubble discovered that light from remote galaxies was redshifted; i.e. the more remote galaxies were, the more shifted was the light coming from them. This observation was quickly interpreted as galaxies receding from earth. If earth is not in some special, privileged, central position in the universe, then it would mean all galaxies are moving apart, and the further away, the faster they are moving away. It is now understood that the universe is expanding, carrying the galaxies with it, and causing this observation. Many other observations agree, and also lead to the same conclusion. However, for many years it was not clear why or how the universe might be expanding, or what it might signify.Based on a huge amount of experimental observation and theoretical work, it is now believed that the reason for the observation is that space itself is expanding, and that it expanded very rapidly within the first fraction of a second after the Big Bang. This kind of expansion is known as the "metric expansion". In mathematics and physics, a "metric" means a measure of distance, and the term implies that the sense of distance within the universe is itself changing, although at this time it is far too small an effect to see on less than an intergalactic scale.The modern explanation for the metric expansion of space was proposed by physicist Alan Guth in 1979, while investigating the problem of why no magnetic monopoles are seen today. Guth found in his investigation that if the universe contained a field that has a positive-energy false vacuum state, then according to general relativity it would generate an exponential expansion of space. It was very quickly realized that such an expansion would resolve many other long-standing problems. These problems arise from the observation that to look like it does today, the universe would have to have started from very finely tuned, or "special" initial conditions at the Big Bang. Inflation theory largely resolves these problems as well, thus making a universe like ours much more likely in the context of Big Bang theory.No field responsible for the cosmic inflation has been discovered. However such a field, if found in the future, would be scalar. The first similar scalar field proven to exist was only discovered in 2012 - 2013 and is still being researched. So it is not seen as problematic that a field responsible for cosmic inflation and the metric expansion of space has not yet been discovered.The proposed field and its quanta (the subatomic particles related to it) have been named inflaton. If this field did not exist, scientists would have to propose a different explanation for all the observations that strongly suggest a metric expansion of space has occurred, and is still occurring much more slowly today.Overview of metrics and comoving coordinates[edit]Main articles: Metric (mathematics) and tensorTo understand the metric expansion of the universe, it is helpful to discuss briefly what a metric is, and how metric expansion works.A metric defines the concept of distance, by stating in mathematical terms how distances between two nearby points in space are measured, in terms of the coordinate system. Coordinate systems locate points in a space (of whatever number of dimensions) by assigning unique positions on a grid, known as coordinates, to each point. GPS, latitude and longitude, and x-y graphs are common examples of coordinates. A metric is a formula which describes how a number known as "distance" is to be measured between two points.It may seem obvious that distance is measured by a straight line, but in many cases it is not. For example, long haul aircraft travel along a curve known as a "great circle" and not a straight line, because that is a better metric for air travel. (A straight line would go through the earth). Another example is planning a car journey, where one might want the shortest journey in terms of travel time - in that case a straight line is a poor choice of metric because the shortest distance by road is not normally a straight line, and even the path nearest to a straight line will not necessarily be the quickest. A final example is the internet, where even for nearby towns, the quickest route for data can be via major connections that go across the country and back again. In this case the metric used will be the shortest time that data takes to travel between two points on the network.In cosmology, we cannot use a ruler to measure metric expansion, because our ruler will also be expanding (extremely slowly). Also any objects on or near earth that we might measure are being held together or pushed apart by several forces which are far larger in their effects. So even if we could measure the tiny expansion that is still happening, we would not notice the change on a small scale or in everyday life. On a large intergalactic scale, we can use other tests of distance and these doshow that space is expanding, even if a ruler on earth could not measure it.The metric expansion of space is described using the mathematics of metric tensors. The coordinate system we use is called "comoving coordinates", a type of coordinate system which takes account of time as well as space and the speed of light, and allows us to incorporate the effects of both general and special relativity.Example: "Great Circle" metric for Earth's surface[edit]For example, consider the measurement of distance between two places on the surface of the Earth. This is a simple, familiar example of spherical geometry. Because the surface of the Earth is two-dimensional, points on the surface of the Earth can be specified by two coordinates — for example, the latitude and longitude. Specification of a metric requires that one first specify the coordinates used. In our simple example of the surface of the Earth, we could choose any kind of coordinate system we wish, for example latitude and longitude, or X-Y-Z Cartesian coordinates. Once we have chosen a specific coordinate system, the numerical values of the coordinates of any two points are uniquely determined, and based upon the properties of the space being discussed, the appropriate metric is mathematically established too. On the curved surface of the Earth, we can see this effect in long-haul airline flights where the distance between two points is measured based upon a great circle, rather than the straight line one might plot on a two-dimensional map of the Earth's surface. In general, such shortest-distance paths are called "geodesics". In Euclidean geometry, the geodesic is a straight line, while in non-Euclidean geometry such as on the Earth's surface, this is not the case. Indeed, even the shortest-distance great circle path is always longer than the Euclidean straight line path which passes through the interior of the Earth. The difference between the straight line path and the shortest-distance great circle path is due to the curvature of the Earth's surface. While there is always an effect due to this curvature, at short distances the effect is small enough to be unnoticeable.On plane maps, great circles of the Earth are mostly not shown as straight lines. Indeed, there is a seldom-used map projection, namely the gnomonic projection, where all great circles are shown as straight lines, but in this projection, the distance scale varies very much in different areas. There is no map projection in which the distance between any two points on Earth, measured along the great circle geodesics, is directly proportional to their distance on the map; such accuracy is possible only with a globe.Metric tensors[edit]In differential geometry, the backbone mathematics for general relativity, a metric tensor can be defined which precisely characterizes the space being described by explaining the way distances should be measured in every possible direction. General relativity necessarily invokes a metric in four dimensions (one of time, three of space) because, in general, different reference frames will experience different intervals of time and space depending on the inertial frame. This means that the metric tensor in general relativity relates precisely how two events in spacetime are separated. A metric expansion occurs when the metric tensor changes with time (and, specifically, whenever the spatial part of the metric gets larger as time goes forward). This kind of expansion is different from all kinds of expansions and explosionscommonly seen in nature in no small part because times and distances are not the same in all reference frames, but are instead subject to change. A useful visualization is to approach the subject rather than objects in a fixed "space" moving apart into "emptiness", as space itself growing between objects without any acceleration of the objects themselves. The space between objects shrinks or grows as the various geodesics converge or diverge.Because this expansion is caused by relative changes in the distance-defining metric, this expansion (and the resultant movement apart of objects) is not restricted by the speed of light upper bound of special relativity. Two reference frames that are globally separated can be moving apart faster than light without violating special relativity, although whenever two reference frames diverge from each other faster than the speed of light, there will be observable effects associated with such situations including the existence of various cosmological horizons.Theory and observations suggest that very early in the history of the universe, there was an inflationary phase where the metric changed very rapidly, and that the remaining time-dependence of this metric is what we observe as the so-called Hubble expansion, the moving apart of all gravitationally unbound objects in the universe. The expanding universe is therefore a fundamental feature of the universe we inhabit — a universe fundamentally different from the static universe Albert Einstein first considered when he developed his gravitational theory.Comoving coordinates[edit]Main article: Comoving coordinatesIn expanding space, proper distances are dynamical quantities which change with time. An easy way to correct for this is to use comoving coordinates which remove this feature and allow for a characterization of different locations in the universe without having to characterize the physics associated with metric expansion. In comoving coordinates, the distances between all objects are fixed and the instantaneous dynamics of matter and light are determined by the normal physics of gravityand electromagnetic radiation. Any time-evolution however must be accounted for by taking into account the Hubble law expansion in the appropriate equations in addition to any other effects that may be operating (gravity, dark energy, or curvature, for example). Cosmological simulations that run through significant fractions of the universe's history therefore must include such effects in order to make applicable predictions for observational cosmology.Understanding the expansion of the universe[edit]Main article: Inflation (cosmology)Measurement of expansion and change of rate of expansion[edit]When an object is receding, its light gets stretched (redshifted). When the object is approaching, its light gets compressed (blueshifted).In principle, the expansion of the universe could be measured by taking a standard ruler and measuring the distance between two cosmologically distant points, waiting a certain time, and then measuring the distance again, but in practice, standard rulers are not easy to find on cosmological scales and the timescales over which a measurable expansion would be visible are too great to be observable even by multiple generations of humans. The expansion of space is measured indirectly. The theory of relativity predicts phenomena associated with the expansion, notably the redshift-versus-distance relationship known as Hubble's Law; functional forms for cosmological distance measurements that differ from what would be expected if space were not expanding; and an observable change in the matter and energy density of the universe seen at different lookback times.The first measurement of the expansion of space came with Hubble's realization of the velocity vs. redshift relation. Most recently, by comparing the apparent brightness of distant standard candles to the redshift of their host galaxies, the expansion rate of the universe has been measured to be H0= 73.24 ± 1.74 (km/s)/Mpc.[8]This means that for every million parsecs of distance from the observer, the light received from that distance is cosmologically redshifted by about 73 kilometers per second. On the other hand, by assuming a cosmological model, e.g. Lambda-CDM model, one can infer the Hubble constant from the size of the largest fluctuations seen in the Cosmic Microwave Background. A higher Hubble constant would imply a smaller characteristic size of CMB fluctuations, and vice versa. The Planck collaboration measure the expansion rate this way and determine H0= 67.4 ± 0.5 (km/s)/Mpc.[9]There is a disagreement between the two measurements, the distance ladder being model-independent and the CMB measurement depending on the fitted model, which hints at new physics beyond our standard cosmological models.The Hubble parameter is not thought to be constant through time. There are dynamical forces acting on the particles in the universe which affect the expansion rate. It was earlier expected that the Hubble parameter would be decreasing as time went on due to the influence of gravitational interactions in the universe, and thus there is an additional observable quantity in the universe called the deceleration parameter which cosmologists expected to be directly related to the matter density of the universe. Surprisingly, the deceleration parameter was measured by two different groups to be less than zero (actually, consistent with −1) which implied that today the Hubble parameter is converging to a constant value as time goes on. Some cosmologists have whimsically called the effect associated with the "accelerating universe" the "cosmic jerk".[10]The 2011 Nobel Prize in Physics was given for the discovery of this phenomenon.[11]In October 2018, scientists presented a new third way (two earlier methods, one based on redshifts and another on the cosmic distance ladder, gave results that do not agree), using information from gravitational wave events (especially those involving the merger of neutron stars, like GW170817), of determining the Hubble Constant, essential in establishing the rate of expansion of the universe.[12][13]Measuring distances in expanding space[edit]This section is written like a personal reflection, personal essay, or argumentative essay that states a Wikipedia editor's personal feelings or presents an original argument about a topic. Please help improve it by rewriting it in an encyclopedic style.(August 2015)(Learn how and when to remove this template message)Two views of an isometric embedding of part of the visible universe over most of its history, showing how a light ray (red line) can travel an effective distance of 28 billion light years (orange line) in just 13 billion years of cosmological time. (Mathematical details)At cosmological scales the present universe is geometrically flat,[14]which is to say that the rules of Euclidean geometryassociated with Euclid's fifth postulate hold, though in the past spacetime could have been highly curved. In part to accommodate such different geometries, the expansion of the universe is inherently general relativistic; it cannot be modeled with special relativity alone, though such models exist, they are at fundamental odds with the observed interaction between matter and spacetime seen in our universe.The images to the right show two views of spacetime diagrams that show the large-scale geometry of the universe according to the ΛCDM cosmological model. Two of the dimensions of space are omitted, leaving one dimension of space (the dimension that grows as the cone gets larger) and one of time (the dimension that proceeds "up" the cone's surface). The narrow circular end of the diagram corresponds to a cosmological time of 700 million years after the big bang while the wide end is a cosmological time of 18 billion years, where one can see the beginning of the accelerating expansion as a splaying outward of the spacetime, a feature which eventually dominates in this model. The purple grid lines mark off cosmological time at intervals of one billion years from the big bang. The cyan grid lines mark off comoving distance at intervals of one billion light years in the present era (less in the past and more in the future). Note that the circular curling of the surface is an artifact of the embedding with no physical significance and is done purely to make the illustration viewable; space does not actually curl around on itself. (A similar effect can be seen in the tubular shape of the pseudosphere.)The brown line on the diagram is the worldline of the Earth (or, at earlier times, of the matter which condensed to form the Earth). The yellow line is the worldline of the most distant known quasar. The red line is the path of a light beam emitted by the quasar about 13 billion years ago and reaching the Earth in the present day. The orange line shows the present-day distance between the quasar and the Earth, about 28 billion light years, which is, notably, a larger distance than the age of the universe multiplied by the speed of light: ct.According to the equivalence principle of general relativity, the rules of special relativity are locally valid in small regions of spacetime that are approximately flat. In particular, light always travels locally at the speed c; in our diagram, this means, according to the convention of constructing spacetime diagrams, that light beams always make an angle of 45° with the local grid lines. It does not follow, however, that light travels a distance ct in a time t, as the red worldline illustrates. While it always moves locally at c, its time in transit (about 13 billion years) is not related to the distance traveled in any simple way since the universe expands as the light beam traverses space and time. In fact the distance traveled is inherently ambiguous because of the changing scale of the universe. Nevertheless, we can single out two distances which appear to be physically meaningful: the distance between the Earth and the quasar when the light was emitted, and the distance between them in the present era (taking a slice of the cone along the dimension that we've declared to be the spatial dimension). The former distance is about 4 billion light years, much smaller than ct because the universe expanded as the light traveled the distance, the light had to "run against the treadmill" and therefore went farther than the initial separation between the Earth and the quasar. The latter distance (shown by the orange line) is about 28 billion light years, much larger than ct. If expansion could be instantaneously stopped today, it would take 28 billion years for light to travel between the Earth and the quasar while if the expansion had stopped at the earlier time, it would have taken only 4 billion years.The light took much longer than 4 billion years to reach us though it was emitted from only 4 billion light years away, and, in fact, the light emitted towards the Earth was actually moving away from the Earth when it was first emitted, in the sense that the metric distance to the Earth increased with cosmological time for the first few billion years of its travel time, and also indicating that the expansion of space between the Earth and the quasar at the early time was faster than the speed of light. None of this surprising behavior originates from a special property of metric expansion, but simply from local principles of special relativity integrated over a curved surface.Topology of expanding space[edit]A graphical representation of the expansion of the universe with the inflationary epoch represented as the dramatic expansion of the metric seen on the left. This diagram can be confusing because the expansion of space looks like it is happening into an empty "nothingness". However, this is a choice made for convenience of visualization: it is not a part of the physical models which describe the expansion.Over time, the space that makes up the universe is expanding. The words 'space' and 'universe', sometimes used interchangeably, have distinct meanings in this context. Here 'space' is a mathematical concept that stands for the three-dimensional manifold into which our respective positions are embedded while 'universe' refers to everything that exists including the matter and energy in space, the extra-dimensions that may be wrapped up in various strings, and the time through which various events take place. The expansion of space is in reference to this 3-D manifold only; that is, the description involves no structures such as extra dimensions or an exterior universe.[15]The ultimate topology of space is a posteriori — something which in principle must be observed — as there are no constraints that can simply be reasoned out (in other words there can not be any a priori constraints) on how the space in which we live is connectedor whether it wraps around on itself as a compact space. Though certain cosmological models such as Gödel's universe even permit bizarre worldlines which intersect with themselves, ultimately the question as to whether we are in something like a "Pac-Manuniverse" where if traveling far enough in one direction would allow one to simply end up back in the same place like going all the way around the surface of a balloon (or a planet like the Earth) is an observational question which is constrained as measurable or non-measurable by the universe's global geometry. At present, observations are consistent with the universe being infinite in extent and simply connected, though we are limited in distinguishing between simple and more complicated proposals by cosmological horizons. The universe could be infinite in extent or it could be finite; but the evidence that leads to the inflationary model of the early universe also implies that the "total universe" is much larger than the observable universe, and so any edges or exotic geometries or topologies would not be directly observable as light has not reached scales on which such aspects of the universe, if they exist, are still allowed. For all intents and purposes, it is safe to assume that the universe is infinite in spatial extent, without edge or strange connectedness.[16]Regardless of the overall shape of the universe, the question of what the universe is expanding into is one which does not require an answer according to the theories which describe the expansion; the way we define space in our universe in no way requires additional exterior space into which it can expand since an expansion of an infinite expanse can happen without changing the infinite extent of the expanse. All that is certain is that the manifold of space in which we live simply has the property that the distances between objects are getting larger as time goes on. This only implies the simple observational consequences associated with the metric expansion explored below. No "outside" or embedding in hyperspace is required for an expansion to occur. The visualizations often seen of the universe growing as a bubble into nothingness are misleading in that respect. There is no reason to believe there is anything "outside" of the expanding universe into which the universe expands.Even if the overall spatial extent is infinite and thus the universe cannot get any "larger", we still say that space is expanding because, locally, the characteristic distance between objects is increasing. As an infinite space grows, it remains infinite.Density of universe during expansion[edit]Despite being extremely dense when very young and during part of its early expansion - far denser than is usually required to form a black hole - the universe did not re-collapse into a black hole. This is because commonly-used calculations for gravitational collapse are usually based upon objects of relatively constant size, such as stars, and do not apply to rapidly expanding space such as the Big Bang.Effects of expansion on small scales[edit]The expansion of space is sometimes described as a force which acts to push objects apart. Though this is an accurate description of the effect of the cosmological constant, it is not an accurate picture of the phenomenon of expansion in general. For much of the universe's history the expansion has been due mainly to inertia. The matter in the very early universe was flying apart for unknown reasons (most likely as a result of cosmic inflation) and has simply continued to do so, though at an ever-decreasing[citation needed]rate due to the attractive effect of gravity.Animation of an expanding raisin bread model. As the bread doubles in width (depth and length), the distances between raisins also double.In addition to slowing the overall expansion, gravity causes local clumping of matter into stars and galaxies. Once objects are formed and bound by gravity, they "drop out" of the expansion and do not subsequently expand under the influence of the cosmological metric, there being no force compelling them to do so.There is no difference between the inertial expansion of the universe and the inertial separation of nearby objects in a vacuum; the former is simply a large-scale extrapolation of the latter.Once objects are bound by gravity, they no longer recede from each other. Thus, the Andromeda galaxy, which is bound to the Milky Way galaxy, is actually falling towards us and is not expanding away. Within the Local Group, the gravitational interactions have changed the inertial patterns of objects such that there is no cosmological expansion taking place. Once one goes beyond the Local Group, the inertial expansion is measurable, though systematic gravitational effects imply that larger and larger parts of space will eventually fall out of the "Hubble Flow" and end up as bound, non-expanding objects up to the scales of superclusters of galaxies. We can predict such future events by knowing the precise way the Hubble Flow is changing as well as the masses of the objects to which we are being gravitationally pulled. Currently, the Local Group is being gravitationally pulled towards either the Shapley Supercluster or the "Great Attractor" with which, if dark energy were not acting, we would eventually merge and no longer see expand away from us after such a time.A consequence of metric expansion being due to inertial motion is that a uniform local "explosion" of matter into a vacuum can be locally described by the FLRW geometry, the same geometry which describes the expansion of the universe as a whole and was also the basis for the simpler Milne universe which ignores the effects of gravity. In particular, general relativity predicts that light will move at the speed c with respect to the local motion of the exploding matter, a phenomenon analogous to frame dragging.The situation changes somewhat with the introduction of dark energy or a cosmological constant. A cosmological constant due to a vacuum energy density has the effect of adding a repulsive force between objects which is proportional (not inversely proportional) to distance. Unlike inertia it actively "pulls" on objects which have clumped together under the influence of gravity, and even on individual atoms. However, this does not cause the objects to grow steadily or to disintegrate; unless they are very weakly bound, they will simply settle into an equilibrium state which is slightly (undetectably) larger than it would otherwise have been. As the universe expands and the matter in it thins, the gravitational attraction decreases (since it is proportional to the density), while the cosmological repulsion increases; thus the ultimate fate of the ΛCDM universe is a near vacuum expanding at an ever-increasing rate under the influence of the cosmological constant. However, the only locally visible effect of the accelerating expansion is the disappearance (by runaway redshift) of distant galaxies; gravitationally bound objects like the Milky Way do not expand and the Andromeda galaxy is moving fast enough towards us that it will still merge with the Milky Way in 3 billion years time, and it is also likely that the merged supergalaxy that forms will eventually fall in and merge with the nearby Virgo Cluster. However, galaxies lying farther away from this will recede away at ever-increasing speed and be redshifted out of our range of visibility.Metric expansion and speed of light[edit]At the end of the early universe's inflationary period, all the matter and energy in the universe was set on an inertial trajectory consistent with the equivalence principleand Einstein's general theory of relativity and this is when the precise and regular form of the universe's expansion had its origin (that is, matter in the universe is separating because it was separating in the past due to the inflaton field)[citation needed].While special relativity prohibits objects from moving faster than light with respect to a local reference frame where spacetime can be treated as flat and unchanging, it does not apply to situations where spacetime curvature or evolution in time become important. These situations are described by general relativity, which allows the separation between two distant objects to increase faster than the speed of light, although the definition of "distance" here is somewhat different from that used in an inertial frame. The definition of distance used here is the summation or integration of local comoving distances, all done at constant local proper time. For example, galaxies that are more than the Hubble radius, approximately 4.5 gigaparsecs or 14.7 billion light-years, away from us have a recession speed that is faster than the speed of light. Visibility of these objects depends on the exact expansion history of the universe. Light that is emitted today from galaxies beyond the cosmological event horizon, about 5 gigaparsecs or 16 billion light-years, will never reach us, although we can still see the light that these galaxies emitted in the past.Because of the high rate of expansion, it is also possible for a distance between two objects to be greater than the value calculated by multiplying the speed of light by the age of the universe. These details are a frequent source of confusion among amateurs and even professional physicists.[3]Due to the non-intuitive nature of the subject and what has been described by some as "careless" choices of wording, certain descriptions of the metric expansion of space and the misconceptions to which such descriptions can lead are an ongoing subject of discussion in the realm of pedagogy and communication of scientific concepts.[4][5][6][7]In June 2016, NASA and ESA scientists reported that the universe was found to be expanding 5% to 9% faster than thought earlier, based on studies using the Hubble Space Telescope.[2]Scale factor[edit]At a fundamental level, the expansion of the universe is a property of spatial measurement on the largest measurable scales of our universe. The distances between cosmologically relevant points increases as time passes leading to observable effects outlined below. This feature of the universe can be characterized by a single parameter that is called the scale factor which is a function of time and a single value for all of space at any instant (if the scale factor were a function of space, this would violate the cosmological principle). By convention, the scale factor is set to be unity at the present time and, because the universe is expanding, is smaller in the past and larger in the future. Extrapolating back in time with certain cosmological models will yield a moment when the scale factor was zero; our current understanding of cosmology sets this time at 13.799 ± 0.021 billion years ago. If the universe continues to expand forever, the scale factor will approach infinity in the future. In principle, there is no reason that the expansion of the universe must be monotonic and there are models where at some time in the future the scale factor decreases with an attendant contraction of space rather than an expansion.Other conceptual models of expansion[edit]The expansion of space is often illustrated with conceptual models which show only the size of space at a particular time, leaving the dimension of time implicit.In the "ant on a rubber rope model" one imagines an ant (idealized as pointlike) crawling at a constant speed on a perfectly elastic rope which is constantly stretching. If we stretch the rope in accordance with the ΛCDM scale factor and think of the ant's speed as the speed of light, then this analogy is numerically accurate — the ant's position over time will match the path of the red line on the embedding diagram above.In the "rubber sheet model" one replaces the rope with a flat two-dimensional rubber sheet which expands uniformly in all directions. The addition of a second spatial dimension raises the possibility of showing local perturbations of the spatial geometry by local curvature in the sheet.In the "balloon model" the flat sheet is replaced by a spherical balloon which is inflated from an initial size of zero (representing the big bang). A balloon has positive Gaussian curvature while observations suggest that the real universe is spatially flat, but this inconsistency can be eliminated by making the balloon very large so that it is locally flat to within the limits of observation. This analogy is potentially confusing since it wrongly suggests that the big bang took place at the center of the balloon. In fact points off the surface of the balloon have no meaning, even if they were occupied by the balloon at an earlier time.In the "raisin bread model" one imagines a loaf of raisin bread expanding in the oven. The loaf (space) expands as a whole, but the raisins (gravitationally bound objects) do not expand; they merely grow farther away from each other.Theoretical basis and first evidence[edit]The expansion of the universe proceeds in all directions as determined by the Hubble constant. However, the Hubble constant can change in the past and in the future, dependent on the observed value of density parameters (Ω). Before the discovery of dark energy, it was believed that the universe was matter-dominated, and so Ω on this graph corresponds to the ratio of the matter density to the critical density ([math]{\displaystyle \Omega _{m}}[/math]).Hubble's law[edit]Technically, the metric expansion of space is a feature of many solutions[which?]to the Einstein field equations of general relativity, and distance is measured using the Lorentz interval. This explains observations which indicate that galaxies that are more distant from us are receding faster than galaxies that are closer to us (see Hubble's law).Cosmological constant and the Friedmann equations[edit]The first general relativistic models predicted that a universe which was dynamical and contained ordinary gravitational matter would contract rather than expand. Einstein's first proposal for a solution to this problem involved adding a cosmological constant into his theories to balance out the contraction, in order to obtain a static universe solution. But in 1922 Alexander Friedmann derived a set of equations known as the Friedmann equations, showing that the universe might expand and presenting the expansion speed in this case.[17]The observations of Edwin Hubble in 1929 suggested that distant galaxies were all apparently moving away from us, so that many scientists came to accept that the universe was expanding.Hubble's concerns over the rate of expansion[edit]While the metric expansion of space appeared to be implied by Hubble's 1929 observations, Hubble disagreed with the expanding-universe interpretation of the data:[...] if redshift are not primarily due to velocity shift [...] the velocity-distance relation is linear, the distribution of the nebula is uniform, there is no evidence of expansion, no trace of curvature, no restriction of the time scale [...] and we find ourselves in the presence of one of the principles of nature that is still unknown to us today [...] whereas, if redshifts are velocity shifts which measure the rate of expansion, the expanding models are definitely inconsistent with the observations that have been made [...] expanding models are a forced interpretation of the observational results.—E. Hubble, Ap. J., 84, 517, 1936[18][If the redshifts are a Doppler shift ...] the observations as they stand lead to the anomaly of a closed universe, curiously small and dense, and, it may be added, suspiciously young. On the other hand, if redshifts are not Doppler effects, these anomalies disappear and the region observed appears as a small, homogeneous, but insignificant portion of a universe extended indefinitely both in space and time.—E. Hubble, Monthly Notices of the Royal Astronomical Society, 97, 506, 1937[19]Hubble's skepticism about the universe being too small, dense, and young turned out to be based on an observational error. Later investigations appeared to show that Hubble had confused distant H II regions for Cepheid variables and the Cepheid variables themselves had been inappropriately lumped together with low-luminosity RR Lyrae stars causing calibration errors that led to a value of the Hubble Constant of approximately 500 km/s/Mpc instead of the true value of approximately 70 km/s/Mpc. The higher value meant that an expanding universe would have an age of 2 billion years (younger than the Age of the Earth) and extrapolating the observed number density of galaxies to a rapidly expanding universe implied a mass density that was too high by a similar factor, enough to force the universe into a peculiar closed geometry which also implied an impending Big Crunch that would occur on a similar time-scale. After fixing these errors in the 1950s, the new lower values for the Hubble Constant accorded with the expectations of an older universe and the density parameter was found to be fairly close to a geometrically flat universe.[20]However, recent measurements of the distances and velocities of faraway galaxies revealed a 9 percent discrepancy in the value of the Hubble constant, implying a universe that seems expanding too fast compared to previous measurements.[21]In 2001, Dr. Wendy Freedman determined space to expand at 72 kilometers per second per megaparsec - roughly 3.3 million light years - meaning that for every 3.3 million light years further away from the earth you are, the matter where you are is moving away from earth 72 kilometers a second faster.[21]In the summer of 2016, another measurement reported a value of 73 for the constant, thereby contradicting 2013 measurements from the European Planck mission of slower expansion value of 67. The discrepancy opened new questions concerning the nature of dark energy, or of neutrinos.[21]Inflation as an explanation for the expansion[edit]Until the theoretical developments in the 1980s no one had an explanation for why this seemed to be the case, but with the development of models of cosmic inflation, the expansion of the universe became a general feature resulting from vacuum decay. Accordingly, the question "why is the universe expanding?" is now answered by understanding the details of the inflation decay process which occurred in the first 10−32seconds of the existence of our universe.[22]During inflation, the metric changed exponentially, causing any volume of space that was smaller than an atom to grow to around 100 million light years across in a time scale similar to the time when inflation occurred (10−32seconds).Measuring distance in a metric space[edit]The diagram depicts the expansion of the universe and the relative observer phenomenon. The blue galaxies have expanded further apart than the white galaxies. When choosing an arbitrary reference point such as the gold galaxy or the red galaxy, the increased distance to other galaxies the further away they are appear the same. This phenomenon of expansion indicates two factors: there is no centralized point in the universe, and that the Milky Way Galaxy is not the center of the universe. The appearance of centrality is due to an observer bias that is equivalent no matter what location an observer sits.Main article: Comoving coordinatesIn expanding space, distance is a dynamic quantity which changes with time. There are several different ways of defining distance in cosmology, known as distance measures, but a common method used amongst modern astronomers is comoving distance.The metric only defines the distance between nearby (so-called "local") points. In order to define the distance between arbitrarily distant points, one must specify both the points and a specific curve (known as a "spacetime interval") connecting them. The distance between the points can then be found by finding the length of this connecting curve through the three dimensions of space. Comoving distance defines this connecting curve to be a curve of constant cosmological time. Operationally, comoving distances cannot be directly measured by a single Earth-bound observer. To determine the distance of distant objects, astronomers generally measure luminosity of standard candles, or the redshift factor 'z' of distant galaxies, and then convert these measurements into distances based on some particular model of spacetime, such as the Lambda-CDM model. It is, indeed, by making such observations that it was determined that there is no evidence for any 'slowing down' of the expansion in the current epoch.Observational evidence[edit]Theoretical cosmologists developing models of the universe have drawn upon a small number of reasonable assumptions in their work. These workings have led to models in which the metric expansion of space is a likely feature of the universe. Chief among the underlying principles that result in models including metric expansion as a feature are:the Cosmological Principle which demands that the universe looks the same way in all directions (isotropic) and has roughly the same smooth mixture of material (homogeneous).the Copernican Principle which demands that no place in the universe is preferred (that is, the universe has no "starting point").Scientists have tested carefully whether these assumptions are valid and borne out by observation. Observational cosmologistshave discovered evidence — very strong in some cases — that supports these assumptions, and as a result, metric expansion of space is considered by cosmologists to be an observed feature on the basis that although we cannot see it directly, scientists have tested the properties of the universe and observation provides compelling confirmation.[23]Sources of this confidence and confirmation include:Hubble demonstrated that all galaxies and distant astronomical objects were moving away from us, as predicted by a universal expansion.[24] Using the redshift of their electromagnetic spectra to determine the distance and speed of remote objects in space, he showed that all objects are moving away from us, and that their speed is proportional to their distance, a feature of metric expansion. Further studies have since shown the expansion to be highly isotropic and homogeneous, that is, it does not seem to have a special point as a "center", but appears universal and independent of any fixed central point.In studies of large-scale structure of the cosmos taken from redshift surveys a so-called "End of Greatness" was discovered at the largest scales of the universe. Until these scales were surveyed, the universe appeared "lumpy" with clumps of galaxy clusters, superclusters and filaments which were anything but isotropic and homogeneous. This lumpiness disappears into a smooth distribution of galaxies at the largest scales.The isotropic distribution across the sky of distant gamma-ray bursts and supernovae is another confirmation of the Cosmological Principle.The Copernican Principle was not truly tested on a cosmological scale until measurements of the effects of the cosmic microwave background radiation on the dynamics of distant astrophysical systems were made. A group of astronomers at the European Southern Observatory noticed, by measuring the temperature of a distant intergalactic cloud in thermal equilibrium with the cosmic microwave background, that the radiation from the Big Bang was demonstrably warmer at earlier times.[25] Uniform cooling of the cosmic microwave background over billions of years is strong and direct observational evidence for metric expansion.Taken together, these phenomena overwhelmingly support models that rely on space expanding through a change in metric. It was not until the discovery in the year 2000 of direct observational evidence for the changing temperature of the cosmic microwave background that more bizarre constructions could be ruled out. Until that time, it was based purely on an assumption that the universe did not behave as one with the Milky Way sitting at the middle of a fixed-metric with a universal explosion of galaxies in all directions (as seen in, for example, an early model proposed by Milne). Yet before this evidence, many rejected the Milne viewpoint based on the mediocrity principle

I’m assuming that by asking how to write an article researching a topic that you mean how to write a college-level research paper on a topic. If that is NOT what you mean, then I hope that parts of my answer will still be helpful anyway.Here are some suggestions on how to write a research paper in 10 steps:1. Choose a topic2. Choose a research question3. Create a thesis statement4. Research your topic5. Evaluate your sources6. Take notes on sources7. Create an outline8. Write a draft9. Edit the draft10. Finalize your paperCHOOSE A TOPICThe first thing you need to do is to choose a paper topic. Maybe you have been assigned a certain topic already--then you can skip this section. But if you need to come up with your own topic, then choose something that interests you. It’s a lot easier to write a research paper on something that is interesting--otherwise it will be boring and you won’t have a lot of motivation to write a good paper.If you need help choosing a topic, then try these ideas:Go to a university library and visit the section where the books in your subject are located. For example, if you are in an Anthropology class, go to the section of the library where the Anthropology-related books are. (If you need help finding the right section, just ask the librarian.) Browse the books for a couple of hours, and see if you find anything interesting.Browse through an introductory textbook on your subject. Typically, each chapter in an introductory textbook is about a different topic—for example, in an Anthropology textbook, there’ll probably be a chapter on economics, a chapter on gender, a chapter on families and kinship, and so on. See if a certain topic interests you.At your university library, browse through a specialized encyclopedia about your subject. For example, if you are in an Anthropology class, then browse through an Anthropology-related encyclopedia. (Ask your librarian where to find a specialized encyclopedia on your subject.) See if any of the topics in the encyclopedia are interesting.Browse the Oxford Bibliographies website for ideas (you can browse by subject). Go to this website: Oxford Bibliographies - Your Best Research Starts Here2. CHOOSE A RESEARCH QUESTIONNow that you have determined a topic to write about, you need to figure out what aspect of the topic you want to focus on. For example, say you want to research influenza. Are you interested in influenza in a certain country? A certain city? Are you considering all ages or just children? Or maybe the elderly? And what specifically about influenza are you interested in— how people decide to go to the doctor for treatment, or how people avoid the flu, if people get their flu shot, or what? There are so many things that fall under the topic of influenza. You need to narrow the topic down even further.One way to narrow down a topic is to consider it from different angles. For example, you can narrow a topic chronologically (by time) or geographically (by place). Using our influenza example, you could narrow it to a certain time frame, like the last flu season. Or you could narrow the topic by place, and only look at influenza in a certain city or country. Try to narrow down your topic into a more specific one.Once you have narrowed your topic down, write what you want to find out about your topic in the form of a question. This is your research question.You need to make sure that your research question is not too big or too narrow. An example of a research question that is too big is: “What can we do to decrease the number of influenza infections around the world?” There is way too much involved in this question for a small research paper.An example of a research question that is too small is: “How many people were infected with influenza in Seattle, Washington (USA) during the last flu season?” This question is easily answered by a simple number, so you can’t write a whole paper about it.Here are some examples of common types of research questions (taken directly from Developing Strong Research Questions | Criteria and Examples):What are the characteristics of X?What are the similarities between X and Y?What is the relationship between X and Y?What are the main factors in X?What is the role of Y in Z?Does X have an effect on Y?What is the impact of Y on Z?What are the causes of X?What are the advantages and disadvantages of X?How well does Y work?How effective is Z?How can X be achieved?What are the most effective strategies to improve Y?3. CREATE A THESIS STATEMENTIn college, you shouldn’t just be summarizing what you read for a research paper (unless that’s the instructions that your professor gave you). You need to make some kind of point, backed up by your research. The main point of your research paper is called the thesis statement. It is the answer to your research question. A thesis statement should be one or two sentences long.For more information on writing thesis statements, check out the University of Illinois at Urbana-Champaign’s website: Writers Workshop: Writer Resources and Indiana University at Bloomington’s website: How to Write a Thesis Statement.Also, try Ashford University’s Thesis Generator at this website: Thesis Generator4. RESEARCH YOUR TOPICNow that you know what your paper is going to be about, you can start researching your topic.The first thing to do is to make a list of keywords relating to your research topic. Think about everything that you know about your topic and come up with a list of keywords to use in researching. For example, say you are doing a project on influenza. You may want to search for the term “flu” along with the medical term “influenza.” For each word on your list of keywords, try to come up with another word that means the same thing (a synonym) and add that to your list of keywords. For example, if one of your keywords is "flu shot,” make sure you also add “influenza vaccine,” because these are different words that mean the same thing.The next thing to do is take your list of keywords and start doing some library research. You need to be looking for journal articles that match your research topic. You’ll need access to a database of journal articles—ask your librarian if you don’t know how to find these kinds of databases in your library. Some examples of article databases are JSTOR and ProQuest, but there are many, many more! Then, start putting your keywords into the database’s search engine and see what you find.But don’t stop there—for each journal article that you find, also check the list of references at the end. The reference list contains the titles of sources that the article’s author used in doing their own background research.So, browse through the list and look for anything that might be related to your own research, and then look up those articles, too. And then check the list of references in THOSE articles for anything that is related to your own research as well. And look up those articles, and so on and so on.Besides searching academic databases, you can also search the internet for information. For example, you can use your keywords to search in Google Scholar, which will bring up reputable sources of information. Just go to https://scholar.google.com/. Another great place to find research articles is ERIC, which stands for Education Resources Information Center. Here is their website: Education Resources Information Center.In addition, you will want to look for books about your topic. Books may be listed in the reference section of your journal articles. You can also find some by searching your university library’s catalog. You can search the internet, too. A great website to search for books is WorldCat: The World's Largest Library CatalogAlso, check specialized encyclopedias for information. Many times, there is a list of references after each entry in the encyclopedia. These sources may be helpful for your paper. For example, you can visit the Oxford Bibliographies website I mentioned earlier, at this website: Oxford Bibliographies - Your Best Research Starts HereAs you look at the articles and books you find, you will probably come up with more keywords to search for. Just add them to your list and keep researching!You’re going to want to have a good system for keeping track of which keywords you have already searched for, and which databases you have already used, which articles and books you have already read, and which articles you have already checked the list of references.It's easy to start losing track of things, so I suggest using a notebook or Word document and making a sort of diary, just briefly listing things you did such as “I searched the ABC database using keyword #1,” “I searched the XYZ database for keyword #3,” etc. And make some sort of list of which articles and books are read, and which still need to be read, and a list of things to do, and so forth to stay organized.5. EVALUATE YOUR SOURCESJust because you found a source of information doesn’t mean that you should automatically include it in your paper. You need to evaluate each source. Here are a few things to look for:First, check to see if the source is actually relevant for your research paper. You might have found a great source, but it may not really provide much information on your specific research topic.If it is relevant, then check the author of the source to see if they are credible. For example, if the source is a peer-reviewed journal article written by someone with a Ph.D. in their field, then that is most likely a trustworthy source. A blog post written by a non-expert might not be a trustworthy source.Check the publication date to make sure that it’s fairly recent. If you are not sure if a source is too old to use, just ask your professor for guidance.Skim the article and determine if the information is fact or opinion. Consider if the information seems well-researched, or if there is simply information without evidence to support it.For more things to look for, check out the University of Southern California’s website: Research Guides: Organizing Your Social Sciences Research Paper: Evaluating SourcesFor some great checklists for evaluating sources, check out these websites:Benedictine University: Research Guides: Evaluating Sources: The CRAAP TestMLA Style Center: https://style.mla.org/app/uploads/sites/3/2018/09/Checklist-for-Evaluating-Sources.pdfExcelsior Online Writing Lab: Evaluation Checklist - Excelsior College OWL6. TAKE NOTES ON SOURCESNow that you have found a bunch of sources, you need to read each one and take notes. You’ll want to have a system of recording notes from each source of information. Sometimes these notes are called “source cards” because they used to be written on 3 by 5 index cards. You can use index cards, or a notebook, or a Word document, or a spreadsheet, or a database document—whatever works for you. If you want to use a database, check out Airtable, which is a free database that you can download onto your computer. (see Airtable’s website at: Airtable: Organize anything you can imagine)Use one index card or one Word page or one database file for each source. List all the bibliographic information for each source on the card or file. For example, if it is a journal article, list the author, article title, journal name, journal issue & page numbers, publication date, URL (if it has one), the date you accessed the URL, and where you found the article (which library, database, etc.)Here’s an example of what it would look like if you used an index card. You can see how all the bibliographic information is noted on the card.Here’s an example of what the database could look like using Airtable.It's a good idea to put a unique code number on each card or file, so you can refer to the article quickly and easily. I like to use a code number made out of the author’s last name, the date of the article, and the title. I use the first 3 letters of the last name, then the 4 digit date, and then the first 3 letters of the article title. So, in this example article below, the code is KOE2014INF. That way, I can group all the papers under the same author together if I need to. Some people like to just number the cards or files consecutively, and that’s fine, just find a system that works for you.Then, it’s time to start taking notes on each source. Use either a new index card or a new page of your notebook or new Word document and assign that card or file a topic. Then, take notes on your first source, using a new card or file for each different topic, and adding the code on the card or file so that you know which source the info came from. Here’s an example using our made-up influenza research project. You could have a notecard with the topic "history of influenza” on the top of it, and all the notes about the history of influenza on it from source #1: (Please note that this card contains made-up information as an example.)And then you could have a notecard with the topic “transmission of influenza” on it, and then all the notes about the transmission of influenza from source #1 on it. (Please note that this card contains made-up information as an example.)After you are finished taking notes on source #1, repeat the process with source #2. Make a series of notecards or files with different topics, each with notes from source #2. Then continue repeating the process for the rest of your sources.Another way to take notes on each article is to summarize the article in your own words in a one-page grid. That way you have all the information about an article on just one page. I created a template that you can use for this purpose--an image is below, and you can download it for free from my website: https://anthropology4u.com/resources/digital-products/7. CREATE AN OUTLINENow that you have read and taken notes on all of your sources of information, it is time to create an outline.First, read through all of your notes, and create a list of all the ideas that you want to put in your paper. Then, put the ideas into categories. You can write the ideas down on notecards and physically group them in different categories. Or, you can open a new Word document file, create category headings, and cut and paste items from your list into the file. So, now you should have a bunch of categories with details (items from the list of ideas) under each.You can also try organizing all your information into a concept map (also known as a mind map). Just google “free mind mapping software” if you don’t already have an app for that. Put main ideas in separate “bubbles" and connect them to “bubbles” containing each supporting point. Below is an example of a mind map, showing the 4 fields of Anthropology, and some of the subfields within each field.Using the groups of notecards, Word file with categories and details, and/or the mind map, create an outline. Your first section of the outline should be the introduction, and the last section should be the conclusion. In the middle is the body of the paper. This is where you will list your main points (the categories). Then, under each main point, list your supporting points (the ideas in each category).Here’s an example of an outline based on the mind map above:1. Introduction1. Interesting opening2. Thesis statement2. Cultural Anthropology1. Legal Anthropology2. Business Anthropology3. Environmental Anthropology4. etc.3. Physical Anthropology1. Osteology2. Paleopathology3. Forensic Anthropology4. etc.4. Archaeology1. Geoarchaeology2. Underwater Archaeology3. Experimental Archaeology4. etc.5. Linguistic Anthropology1. Descriptive Linguistics2. Ethnolinguistics3. Sociolinguistics4. etc.6. Conclusion1. Summary2. Thesis StatementFor more information on creating an outline, check out this website: How to Create a Structured Research Paper Outline (with example)8. WRITE A DRAFTWrite a first draft, based on your outline. Don’t worry too much about making everything perfect--it's just a rough draft.As I mentioned previously, your paper should have an introduction, a body, and a conclusion.In the introduction, you introduce the topic you are researching, in a paragraph or two. Try to get your reader’s attention in the introduction. Some ways to do this are by providing a quotation, anecdote, interesting fact, or surprising statistic. Also explain any background information the reader needs to know. Then, introduce your main point--your thesis statement-- which is usually placed at the end of the introductory paragraph.In the body, you explain or prove your thesis statement. This part will be several paragraphs long. Each supporting point you make should have its own paragraph, where you expand on the point and give evidence or examples.For each supporting point you make, you should have a few sources to back up what you are saying. Make sure that you are giving your sources credit for their ideas. You need to cite your sources in the text of the paper, not just in a bibliography page at the end. Use whatever citation style your professor or discipline requires. Check out the Purdue Online Writing Lab for information on different styles: Research and Citation Resources // Purdue Writing LabIt’s also a good idea to put in a few direct quotes to help illustrate your points as well--just be sure to cite the sources correctly. Check out this website for more information on using quotes: Working with QuotationsAlso, make sure to link one paragraph to the next with transition words, such as “also," "in addition," “however," "as a result,” “finally," etc.In the conclusion, you summarize everything and restate your thesis statement, all in about one paragraph. You can also explain why your thesis statement matters, and/or what the bigger implications are.On the final page(s) is the references (or bibliography). This is where you list all the sources that you used in the paper. Follow your instructor’s requirements for this section of the paper--they may want the references in APA style, MLA style, Chicago style, or something else.When the first draft is finished, take a break and do something else for a while. This break can be a few hours or a day or two or longer--everyone does something different. Then, you can go back to your draft and look at it again through fresh eyes, and revise it.9. EDIT THE DRAFTRead through your paper and ask yourself if everything makes sense. Check to see if the flow of one paragraph to the next is logical. Consider if your main point is well supported by your supporting points. Try reading your paper out loud to see how it sounds.Look carefully for errors in spelling or punctuation. It’s also a good idea to run your draft through a grammar check, too--try Grammarly’s free version: Write your best with Grammarly.Double-check that all sources have been cited appropriately in the text (otherwise, you may be accused of plagiarism!). Also, double-check your list of references for errors as well.10. FINALIZE YOUR PAPERAfter you have made all the edits to your paper, once again take a break. After your break, take yet another look at your paper. Read it over again, looking for any last-minute errors, writing that doesn’t make sense, etc. Read it out loud again as well, to make sure everything flows as you want it to. Make any last-minute edits. Then, your paper is finished!Make sure to create a backup copy of your paper, and email a copy to yourself as well. That way, if anything happens to your original copy, you have a backup. Or, if you forget to take your printed-out paper to class, you can print another copy at the last minute on campus with the copy in your email. Turn in your assignment and congratulate yourself on completing the research paper!