Martin

Here's how this thread began: It is not contrary to normal science practice to expect people to have a basic knowledge of the conventional standard theory, especially if they want to deviate from it, or go beyond it. Nobody expects you to believe any particular theory. Believe what you want. Criticize the standard model all you want too. But understand what you are criticizing. We have an educational responsibility to explain the consensus cosmology that just about any professional cosmologist assumes as a working model. Because when professionals talk and write they are assuming those concepts. And they are the most vigilant critics as well---you get extra respect points if you can find some observation that calls the standard model into question or suggests some needed modification. A common point of departure is normal science practice. In fact that's the basic reason for this thread!

One of the things that we should be able to calculate is the size of the observable, compressed to Planck density. You should also be able to calculate the critical density from today's Hubble rate of 71 km/s per Mpc. It is about 0.85 nanojoules per cubic meter. If anyone wants to see the calculation please ask. It's easy. The usual estimate of matter density is 0.27 of critical. So that comes to about 0.23 nanojoules per cubic meter. What we need to know is the ratio of Planck density to that. The cube root of that ratio will be how much we shrink the radius of the observable. Planck energy density ( http://en.wikipedia.org/wiki/Planck_units ) is c^7/(hbar*G^2) So we just type this into google: (c^7/(hbar*G^2))/ (0.23 nanojoule/cubic meter) We should get some huge number. Yes! we get 2.0 x 10123 The radius of the observable is currently 46 billion LY. It has to be shrunk by the cube root of that huge number. We should get something like the size of a proton, if I remember right. So let's take the cube root. Put this into google: ((c^7/(hbar*G^2))/ (0.23 nanojoule/cubic meter))^(1/3) We get 1.26 x 1041. So now let's shrink the radius of the observable by that factor. Put this into google: 46 billion light years/ (1.26*10^41) What I get is 3.5 x 10-15 meters. 3.5 femtometers. The proton Compton wavelength is 1.32 femtometers. Actually in the bounce cosmology models they find the bounce happens at some fraction of Planck density. So it wouldn't go quite that high and the size wouldn't be quite that small. But this is a good ballpark figure. You can interpret it by comparison with nuclear particle sizes however.

Questions keep coming up about the usual global time in cosmology. For example someone asks how can someone anywhere in the universe tell this time? There are various ways, like measuring the temperature of the Background for instance. It declines as a predictable function of time, so you can tell time by it. Admittedly crude because temperature measurement is only so accurate, say to within one part per million. So your clock would only be accurate one part per million which is not very good. But its the concept. Another way to tell universe-time is to measure the Hubble rate. This also is crude. It is around 71 currently. (The units they measure it in are an historical accident, not especially convenient, but that's how it is.) I decided that I'd tabulate some expected future values of the Hubble rate. age scale estim. Hubble rate 13.7 1.00 71.0 14.1 1.04 69.0 14.6 1.08 68.2 15.1 1.11 67.5 15.6 1.15 66.9 16.1 1.20 66.2 16.7 1.24 65.6 17.3 1.29 65.1 17.9 1.35 64.6 18.5 1.40 64.1 19.2 1.47 63.7 19.9 1.54 63.3 20.6 1.615 62.9 21.5 1.70 62.55 22.3 1.79 62.25 23.2 1.90 62.0 24.2 2.02 61.7 25.2 2.15 61.5 The scale ratio is just how I'm keeping track of the expansion. The age is currently 13.7 (billion years) and by the time it is 24.2 longrange distances will have doubled, increased by a factor of about 2.02. That means the Background temperature will be half what it is now. 2.728 kelvin/2.02 = 1.35 kelvin. So if you should suddenly be transported to some other unknown location in the universe, and some other time in the future, and you want to know what time it is, then you can see all you need to do is measure the background temperature. If it is 1.35 kelvin then you know you have been transported to year 24.2 billion. It's obviously absolute and it is based on general relativity---the Friedman solution to the basic GR equation. Likewise if instead of measuring the temperature you look around and compare distances and redshifts and measure the Hubble rate (just like Hubble did) and if you find that it is 61.7 km/s per megaparsec (or whatever units the aliens on that distant future planet are using) then you can say immediately that you are in year 24.2 billion. It isn't especially accurate but you an tell the time by looking at the sky---whenever wherever in the universe.

It might sometime interest folks to look into the beginning of the expansion cosmo model. Here's a facsimile of page 1 of Friedman's 1922 paper: http://www.springerlink.com/content/l23864w241673530/fulltext.pdf?page=1 Here is a scan of the entire 10-page paper http://edocs.ub.uni-frankfurt.de/volltexte/2008/9863/pdf/E001554876.pdf I see he makes a rough estimate of the age of the expansion---he says 10 billion years---gets it roughly right! Friedman's work was not based on redshifts. An American astronomer Vesto Slipher had previously measured some galaxy redshifts but had not discovered their correlation with distance. Later on, Hubble was able to estimate distances and thus to correlate redshift with distance and find the linear proportion connecting them (Hubble's Law 1929). It is interesting that the expanding universe idea came before the discovery of Hubble's Law. There is no indication that Friedman knew of Slipher's redshift measurements: he arrived at the expansion model on theoretical grounds, based on General Relativity (1915). An English translation of Friedman's 1922 paper is here, but it is pay-per-view http://www.springerlink.com/content/427ex54m3v50/?sortorder=asc&p_o=10 Willem de Sitter came up with an expanding universe model in 1917. Here is a link to one of two papers he wrote that year: http://www.digitallibrary.nl/proceedings/search/detail.cfm?startrow=1&view=image&pubid=2024&search=&var_pdf=&var_pages= Fortunately the paper is in English. The last page is missing in this free digital library copy. De Sitter seems to have a more abstract theoretical interest. I don't see him treating his model as a possible fit to reality. It is of interest as a possible solution to the equation of General Relativity, and an alternative to Einstein's static model. Friedman, on the other hand, plugs some real numbers in and makes a bold attempt to get a rough fit. Neither of them seem aware of redshift information.

Here's an alternative link to the "Misconceptions about the Big Bang" article from the March 2005 SciAm that has proven generally useful: http://www.astro.princeton.edu/~aes/AST105/Readings/misconceptionsBigBang.pdf The one I've been using has a black page at the beginning of the pdf file, which might confuse people. http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf

The most recent values of cosmo model parameters are here http://arxiv.org/abs/0803.0547 Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation E. Komatsu, J. Dunkley, M. R. Nolta, C. L. Bennett, B. Gold, G. Hinshaw, N. Jarosik, D. Larson, M. Limon, L. Page, D. N. Spergel, M. Halpern, R. S. Hill, A. Kogut, S. S. Meyer, G. S. Tucker, J. L. Weiland, E. Wollack, E. L. Wright (last revised 17 Oct 2008) For instance this gives 95% confidence intervals for the curvature parameter Omegak. See table 2 on page 4*. These are based either on WMAP data alone or WMAP (microwave background) taken together with SNe (supernovae) and BAO (galaxy counts at various distances---redshift surveys). The usual practice is to quote WMAP+BAO+SNe figures, because based on all relevant data and considered most reliable. No one should suppose that we are talking about the actual universe here. We are talking about best fit models. The values of the parameters that give the best fit to millions upon millions of datapoints. Getting the mathematically simplest model that gives the best fit. This is what cosmology about, not verbal concepts or philosophy or even mental pictures, although pictures can help visualize the model. If you are used to talking with people about Omegatot, the total Omega**, it will help you make sense of Table 2 to know that Omegak = 1 - Omegatot. So the positive curvature case, the spatial closed universe, which has Omegatot > 1, is the case where Omegak < 0. It is a quirk in the notation, positive curvature corresponds to Omegak negative. All standard cosmo models are edgeless in other words boundaryless. This is whether or not they are finite spatial volume. Boundaries would screw up the physics, add unnecessary complication, and provide no improvement to the data-fit. Almost the only finite volume case ever considered is the positive curved hypersphere. The 3D analog of the 2D balloon surface. There is a rarely discussed flat model with finite 3D volume sometimes called "pacman" which is a cube with opposite sides equated so that running off thru the right wall makes you come in thru the left wall. There is no sign of any such funhouse wall of mirrors stuff going on in the real universe so people normally ignore "pacman". Typically it's taken for granted that Omegak = 0 means infinite 3D volume. This case, the flat infinite volume, is the easiest to calculate with and, since it provides a decent fit, widely favored. But the positive curved hypersphere case is not ruled out and may give a marginally (not statistically significant) better fit to the data. *Here is the 95% confidence interval they give on page 4: −0.0179 < Ωk < 0.0081 You can see it is tilted in favor of negative Omegak, which means positive curvature, the finite volume 3D spherical case. But only by about 2 to 1. Still not significant. Could go either way. A new spacecraft, the Planck, is planned for launch this year. Should further narrow down the limits. **Omegatot is the ratio of the total energy density, the measured largescale average density of all forms, divided by the critical density which the universe would need to have in order for space to be exactly flat. Omegatot = 1 signifies the spatial flat case, zero curvature. Omegatot > 1 is the positive curved case where space is a 3D analog to surface of a sphere. The critical energy density is easy to calculate from the Hubble rate H. It is simply 3c2H2/(8 pi G). If you ever want to know it, just type 3 c^2 (71 km/s per Mpc)^2/(8 pi G) into google and it'll be calculated for you. If you like some other value of the Hubble rate, put that in instead of 71 km/s per Mpc.

Wow. That's both gratifying and unexpected.

We have now derived formulas for several Planck units and in particular we have force (c^4/G) and the area (hbar*G/c^3) So let's divide and get the Planck unit pressure (c^4/G)/(hbar*G/c^3) which simplifies to c^7/(hbar*G^2) Let's put that into google to check that it is a pressure. Yes it comes out to 4.6 x 10113 newton per square meter (try it!) And newton per square meter is the same as joule per cubic meter---we have found the Planck unit of energy density, as well. Namely the Planck energy density is c^7/(hbar*G^2). Example 1 In contemporary quantum cosmology models where there is a bounce, the bounce commonly happens at about 40 percent of the Planck energy density. That would be 40 percent of 4.6 x 10113 joules per cubic meter. Just as a simple illustration, we have used the google calculator to find the energy density at the onset of expansion, in a common sort of QC model. Example 2 How much have volumes expanded since the bounce? For simplicity I'll ignore inflation. The present critical energy density is 0.85 nanojoule per cubic meter and excluding dark energy this is 0.23 nanojoule per cubic meter. What is the ratio of energy densities? I put this into google 0.4*4.6*10^113/(0.23*10^-9) and it came out with 8 x 10122 ==================== Norman, thanks for your interest, but I think this attempt at a google-calculator based tutorial on Planck units is not serving a useful purpose---except for yours, no comments, no questions. I am going to let it sit for a while and see. If no more interest then I will unsticky and let it drift off.

Congratulations to you Norman. My project here is more casual/inconsequential.

Norman your stuff is more specialized/advanced than fits in to a basic tutorial like this. It could be that there is no interest---nobody who doesn't know the simplest Planck units, and wants to learn them, is reading. If there is no market I will just let it drop. If I don't let it drop I want to take things kinda slow and methodically. So far all we have done is the Planck force c^4/G and noted that hbar*c is a natural quantity of area multiplied by force. So that dividing hbar*c by c^4/G we get the Planck unit of area. And that gave us the Planck length, just taking square root of the area. Then multiplying force by length, we get the natural unit of energy. Planck energy is as far as we've come so far. What is another really basic Planck unit that is simple to write? What about the natural unit of pressure? Pressure is force divided by area, so to get Planck pressure all we need to do is divide two things we already have, force and area.

It's advisable not to refer to the BB as the "origin" of the universe because scientifically speaking the classic BB model describes the early universe back to within a few planck times of where it fails, but does not describe anything that could be called an initial state or a beginning. Talking as if the model describes a precise beginning (at some putative t=0) is incorrect, and it can easily confuse noobs---and lead to sterile argument. Math models in physics commonly have a domain of applicability---the only give sensible answers well within certain limits. If you push them too close to their limits you can't trust the numbers the model gives you. Classic GR and the classic cosmology model is not reliable once you get within a few planck times of t=0. Amd at t=0 it simply doesn't compute (that is in fact how the time-marker t=0 is defined.) So the classic BB model is acknowledged to be incomplete. It has no origin or initial state. Current research is aimed at extending the BB model to the t=0 point and beyond. The new BB models also do not describe the "origin" of the universe. They simply go back further in time. Typically what is found is space time and matter obeying the same laws. In some, there is no scientific reason to postulate a "beginning" of the universe. It is incorrect to talk about an origin whether in the classic context of the old BB model or in the context of the new BB models. None of the models involve a beginning or an initial state. So the word "origin" quite possibly is without meaning (applied to the universe). Of course it can be meaningful to talk about the start of expansion. That is a well-defined event at least in some models. But in those models the start of expansion is not the beginning of the universe, because they describe prior process leading up to the start of expansion. So it is legitimate to talk about the beginnings of various phases occurring in some stated BB model. But when talking about BB theory it's not so good to be referring to the "origin of the universe".

Thanks for the response, Norman! Now I'll boil the first post down to essentials and move on. What I want is that we all are sufficiently familiar with how the Planck units arise in nature that we can construct them from scratch, without looking up the definitions. In this approach the only thing you really need to memorize is c^4/G. We all know c already and we know c is the natural unit of speed. So what we need to learn in addition is c^4/G is the natural unit of force. ======================= Before I was urging you try calculating things like hbar*c and c^4/G in terms of all sorts of units---inch, pound, foot, mile, etc etc. The natural unit quantities are built into nature and they are the same whatever random human units you choose to express them in. Now I've made that point, so let's forget it. We can do everything or almost everything just using the usual metric units that the google calculator uses in default mode, when you don't specify. ========================= So to proceed, you should know that hbar is a product of energy and time---often given in joule-seconds. And therefore hbar*c is a product of energy and distance----and thus equivalently a product of force and area. Anybody who has difficulty seeing that hbar*c is a force x area quantity please ask for discussion! I can give more explanation In fact, just as c is the natural unit of speed, hbar*c is the product of the natural unit of force multiplied by the natural unit of area. That's important to realize. What that does for us is it lets us divide out the natural unit of force and get the natural unit of area. You should do this hands-on, yourself, if you haven't already. Use Google to calculate hbar*c/(c^4/G) It should come out in square meters unless you tell the calculator otherwise. Now it is just basic algebra to simplify nature's unit of area to hbar*G/c^3 NOW WE CAN CALCULATE THE NATURAL UNIT OF ENERGY. The simplest way of imagining doing a given amount of work, applying a given amount of energy, is to push with a certain force for a certain distance. Our natural unit of force is c^4/G. Our natural unit of distance is sqrt(hbar*G/c^3) So this is a no-brainer. Just put this into the Google calculator. (c^4/G)sqrt(hbar*G/c^3) That will give you nature's unit of energy a.k.a. Planck energy. If you want Planck mass as well, then just use E = m c^2 to get it. Notice that the blue formula for the Planck energy unit can be simplified considerably. You can consider that homework. We will get to it next time. DOES ANYBODY HAVE ANY QUESTIONS SO FAR?

Planck units like the mass and length come up all over the place in modern physics---they are not the only system, there are other convenient special purpose units, but they are worth getting familiar with. Using the google calculator we can take a kind of almost experimental approach to planck units, explore, build up our concepts, try them out. It is easy---a few posts will show what I mean. So here's a brief tutorial. 1. get to know hbar (Planck's constant) Think of hbar as being the product of amounts of energy and time. Check that by typing things like this into google hbar/minute hbar/year It will give you answers in energy terms----small amounts of energy. If you like BTU or calories or foot pounds you can always ask for the answer in those terms hbar/hour in foot pounds Personally I am most comfortable with ordinary metric units like second meter joule newton, but I want to emphasize that the google calculator works with a wide range of units and will give you answers in pretty much any units you happen to like. It knows how to convert and it does what you tell it. 2. Think of hbar as the product of (typically small) amounts of force x distance x time. Try pulling hbar apart using the calculator. Take hbar, pull out some length, then pull out some time (hbar/inch)/day It will always turn out to be a force. Let's have the answer come out in pounds of force: (hbar/inch)/day in pounds (hbar/foot)/hour in pounds Try putting the blue thing into google and see. More later Merged post follows: Consecutive posts merged This is the second post of this tutorial. The title of the post is Your first planck unit--the Force :-D 1. Try putting this into google c^4/G Again, to emphasize that there's no metric bias, put this in c^4/G in pounds c^4/G is a natural amount of force. It's the Planck force. Remember it. 2. Besides the Planck force we don't have very much we have to remember. You already pulled apart hbar and you know it is made up of force x length x time Well what other natural constant do you know that involves length and time? c c is length/time So what happens if you multiply force x length x time together with length/time? You get force x area. So let's try that. Multiply hbar*c and check to see if it is the product of some force with some area. The way we check is we put this in google: hbar*c/square inch That is, we multiply hbar and c together and then divide out any amount of area we please, square foot, square meter, square inch, square mile whatever. If hbar*c is the hidden product of some force with some area, then if we divide out some area we should get a force. Just to show we're not biased let's get it in pounds hbar*c/square inch in pounds Merged post follows: Consecutive posts mergedThis is the third post in this short tutorial. The title of the post is Your second planck unit---the Area OK we picked apart hbar a little and we know it acts like it's made of a bit of force multiplied by other stuff. And we teased apart hbar*c some and we know it acts like it is a force x area quantity... made of a small amount of force multiplied by some area. And we know c^4/G is a force. It is a natural amount of force that doesn't involve any man-made units like inch or hour or foot etc. So let's divide hbar*c by that natural force and see what we get. Put this into google hbar*c/(c^4/G) or even better put this in hbar*c/(c^4/G) in square inches That is a natural amoung of area that doesn't depend on man-made stuff like joules kilograms etc. It's expressed in square inches, OK, but that doesn't matter, you could choose any unit of area to express it in---square yards, square millimeters... The quantity of area itself is natural. And if you took highschool algebra you probably noticed that something could be simplified by canceling a c. hbar/(c^3/G) in square foot And we can make it look nicer by flipping the G up hbar*G/c^3 in square miles Your third Planck unit---the Length. Try this in google sqrt (hbar*G/c^3 ) in miles

I want to add a couple of things to the cosmo basics thread: A. what to learn from the balloon picture of expanding distances. B. Lineweaver's Figure 1 from his 2003 paper---how the horizon has evolved. A. Balloon picture http://www.astro.ucla.edu/~wright/Balloon.html http://www.astro.ucla.edu/~wright/Balloon2.html Probably over half of us SFN members have at one time or another advised someone else to imagine an expanding balloon as a way of understanding how space geometry changes with time. How distances between stationary points increase. Like any analogy, not to overinterpret or take too far. Space is not a material as far as we know, not like rubber. The simplest idea of space is it is just a bunch of distances. The balloon with dots stuck on for galaxies is a 2D analog of 3D space. It teaches about the STANDARD no-frills version of cosmology. What can one learn by studying the balloon image. 1. no edge, no boundary, matter distributed uniformly throughout space (for the infinite version just picture a *really* big balloon but it's OK to learn on the finite version) 2. all existence is on the balloon surface, no other dimensions, no other directions you can look or point in. 3. idea of being stationary with respect to the CMB, the matter which radiated the CMB. the CMB is symmetric around you with no doppler hot or cold directions, the expansion is symmetric around you, you are at rest wrt the universal rest frame. this corresponds to staying at the same latitude and longitude on the balloon. that is what the galaxies do. the photons of light move among the galaxies, they are not at rest. (watch Wright's balloon animation and get this image in mind) 4. all largescale distances between stationary points (outside stable structures like galaxies, in which stuff is gravitationally bound together) are increasing by a certain percentage per minute---or per million years. that's Hubble law. Currently 1/140 of a percent every million years but the rate changes. Distances between stationary points increase faster the larger the distance is. Look at the balloon animation. 5. Locally nothing MOVES faster than the photons of light. In spite of the fact that the individual galaxies get farther apart they are not moving in the way the photons are. The photons wriggle past them always at the same speed of 1 inch per minute or whatever. The balloon animation can help you visualize the pattern of changing distances, and how the matter which radiated the CMB which we are now receiving is today 46 billion lightyears from us. B. Lineweaver graph of a shifting cosmo horizon (there was a question about this thx to BabyAstronaut, so I've included a brief explanation.) http://arxiv.org/abs/astro-ph/0305179 Download the PDF and look at page 6, Figure 1. The top section is drawn in real physical distance (instantaneous segmented radar distance between points stationary wrt CMB) The other two sections are special-purpose re-mappings. Let's focus on the top section. Notice that past lightcones are teardrop shape. Notice how the Hubble radius is increasing and asymptotically meets the cosmological event horizon. If we use typical standard model parameters the limiting value for both is 16 billion lightyears. That comes from the Friedmann eqn. The Hubble radius at time t is c/H(t). H(t) --> sqrt(0.73)H(now) as t --> infty Hubble radius --> 13.77/sqrt(0.73) billion lightyears = 16 billion lightyears. If anyone is interested I'll go into more detail, if not, won't waste time. Point here is that you can learn a lot of basic cosmology just by studying the balloon analogy and Lineweaver's 2003 Figure 1. Ask questions if you want to pursue this. http://www.mso.anu.edu.au/~charley/

Before posting on cosmo topics consider getting squared away on the conventional standard version. There are several great tutorials, for which I'll post link. And the standard model universe is embodied in some online calculators---playing around with them gives you some hands-on experience with redshifts, recession speeds, distances and so forth. Here's the authoritative up-to-date Einstein-Online tutorial on cosmology, written in understandable non-mathy language. http://www.einstein-online.info/en/spotlights/cosmology/index.html It is the cosmology part of a broad outreach site maintained by the Albert Enstein Institute, a worldclass science outfit in Germany. Here is the main Einstein-Online index in case you want to look at their other stuff: http://www.einstein-online.info/en/spotlights/index.html An article that has been recommended a lot by many different SFN posters is this one by Lineweaver and Davis http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf It was published March 2005 by SciAm---the Einstein-Online material is more recent and more comprehensive but Lineweaver article is still useful. It is used in a Princeton astro course, so an alternative copy is available online at princeton.edu if this Aussie National University link should ever not work. It makes understanding cosmology much easier if you train your imagination to think visually about changing distances. The Hubble law is a pattern of increasing distances between stationary objects (galaxies are taken as approximately stationary and the distances between widely separated ones increase at a regular percentage rate.) A good way to train your imagination to visualize changing distances is to use Ned Wright's computer animation balloon visuals. If you ever need the links, they are the first two google hits with "wright balloon model". I will give the links but all Ned Wright's stuff on cosmology is really easy to google, so I hardly need to. I'd advise anyone new to cosmology to spend a few minutes with each model. Galaxy stationary means it stays at the same latitude and longitude on the balloon. The wriggling photons of light are not stationary, they gradually creep across the empty space between galaxies. If you have this visual thing well assimilated, a lot of what you encounter in cosmology won't seem surprising or incredible. http://www.astro.ucla.edu/~wright/Balloon.html http://www.astro.ucla.edu/~wright/Balloon2.html Before you post your own personal cosmology ideas I would suggest you take the time to understand the standard version. This may mean that you start off at this forum asking questions rather than immediately expressing your own views. The point is to have a secure understanding of what you deviate from, as a kind of home base. It makes communication more efficient if there is a shared understanding of the mainstream picture. One thing that everybody should have done, who wants to talk cosmology, is play around with the online cosmo calculators. It's an easy way to get to know standard cosmology because that is what is built in to the calculators. The Ned Wright version is the google hit you get with "wright calculator". I'll give the link here as well, even though it is so easy to google: http://www.astro.ucla.edu/~wright/CosmoCalc.html Personally I like a different one, Morgan's cosmos calculator, so I'll give the link to that too: http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html The labels on this one are less technical and some people find it easier to immediately pick up and use---user friendly. The only downside is that at the beginning of every session you have to type in three numbers: .27, .73, and 71. These are standard cosmology parameters. Ned Wright puts them in for you as default settings, but Morgan makes you type them in. Those already experienced with this will recognize these numbers as the matter fraction, the dark energy fraction, and the Hubble rate. That's all we need for starters I think. What I plan to do is discuss some of these things I've mentioned in the next few posts, and encourage everybody who wants to post in cosmo forum to get familiar with these basics. ================================================================== ================================================================== ***end of preceding post*** ================================================================== ================================================================== The desired header on the new post is Cosmo Bronco--a crash course in basics, or for some a refresher Ideally for the sake of reader-friendliness, the following should be a separate post: the #2 post of the thread. Since I can't make it a separate post, please think of it as separate. ================================================================== ================================================================== ***start new post*** ================================================================== ================================================================== There are different ways to approach this material, to suit various people's needs. There's this crash course, for people who are up for it. I'll describe that way in, and then we can talk about more gradual approaches. The crash course goes like this. We assume you have visited the Einstein-Online cosmology site and read some stuff there that interested you. We assume you know the FRW metric, the distance function, that tells timevarying distances between stationary objects, and the scalefactor a(t) that plugs into the metric and as it increases causes spatial distances to increase. We assume you know that the redshift is (one less than) the factor by which distances have increased while the light was in transit. It is a convention to deduct one, so that to get the ratio of distance now to distance then you have to add one to z. z+1 = a(now)/a(then) the factor that distances are bigger by, now as we receive the light versus then when the light was emitted. And we assume that you know the CMB redshift is about 1090. that is a conventional figure for it. So you go to wright's calculator and plug in 1090 http://www.astro.ucla.edu/~wright/CosmoCalc.html Now your job, if you choose to be a volunteer member of the crash course, is to interpret what you see in the calculator windows, when you put in z=1090 (and click the button to make it calculate). If you can interpret even half of what the calculator gives you, then you pass the course Any takers? PS: You might also try z = 1090 in Morgan's http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html remembering that in that case you have to type in the numbers .27, .73, 71 that Wright's gives you automatically. Morgan rounds off its answers and uses more self-explanatory labels, so it is less precise and at the same time more accessible. If you don't have the URL handy, an easy way to get to Morgan's is simply to google "cosmos calculator" Be sure to include the final S on "cosmos".

I was under the impression that sometime around 2004 they changed the system at arXiv so that you needed sponsors. I may be wrong. It is not a quality guarantee thing, in effect IIRC they 'grandfathered in' whoever had already been submitting stuff---even tho it was well-known that plenty of stuff being posted was worthless. the aim of arxiv is to open and not (very) selective. it is just preprints, and they often get revised several times before publication (you see several versions on arxiv). the real selection process comes later. but there are limits. they didnt want the system to get completely overloaded so they put in this "sponsor" requirement. It is a very very low hurdle. there are a huge number of "gate-keepers"----all those people who were uncritically grandfathered-in. BTW this is just my impression. lucaspa may be right and there might not be a sponsorship requirement In case I am right, however, here is how to find a sponsor: look at the abstract of some paper in your area of interest, maybe one you like. one of the links on the abstract page will say (which of the authors of this paper is a sponsor?) click on that. if it is a paper by somebody who has been writing to arxiv for some long time then he may be a potential sponsor, this gives the name of a designated person who can sponsor, so then find out the email of that person and write to them saying that you need a sponsor for your paper