## How is molecular hydrogen detected?

 Quote by Chronos Twofish-Quant is our supernova expert, I'm certain he could shed light on this issue.
Not much. This is an ISM question and not a supernova question. :-) :-)

One thing that I found rather surprising is that it turns out that early universe chemistry is incredibly complicated.

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 Quote by vociferous I'm assuming that the Jean's Mass formula is still applicable. I am assuming that you are referring to the density of the universe, not an individual galaxy. While galaxy formation is still something of a mystery, I believe I am correct in stating that early in a galaxy's formation, it is in the process of overall increasing its density, not decreasing it. I do not really know how that might affect the density of molecular clouds, but you could certainly research it in the published literature. Remember, the density of the universe is not necessarily linearly proportional to the density of early galaxies or the density of the regions where globular clusters formed. For instance, the density of the visible universe is still decreasing, but the density of the Milky way is constant. It seems like a reasonable hypothesis. The question is, where is the evidence? Showing a correlation between density and formation of clusters does not actually support your hypothesis. You need to model how the clusters formed and how the density of the universe would affect their formation. I believe others have theorized this in regards to current stellar evolution. You might want to research papers on supernova-induced star formation if you have not already.
I bolded a few statements here; mainly I need to model how the clusters formed and how the density of the universe would affect their formation.

I don't have a quantitative model, but I can qualitatively describe three distinct stages--perhaps four.
Stage 1--Universe Age: Very young. Galaxy forming stage. Extremely high density. Perturbation caused by supernova results in a gravitational gradient sufficient to overcome outward Hubble-velocity.
Stage 2--Universe Age, Less than a billion years. Globular Cluster forming stage: Medium density. Perturbation caused by supernova results in clumping of matter into stars, but insufficient to overcome outward Hubble-velocity.
(Stage 3)--Universe Age--Current. Spiral forming stage. Superluminal jets fire into already swirling gasses, causing it to clump into stars.
Stage 4--Universe Age--Current. Diffuse stage. Supernova explosion is not sufficient to cause clumping into stars

I made a little video to see if I could make this clearer:
http://screencast.com/t/QxU3YaeWAkXM

I hope this makes clear some of the other differences between this model and your model.
(1) in my hypothesis, the overall density of the universe equal to the overall density of a galaxy or a globular cluster at any given time. The difference is not in density but in clumpiness.
(2) You are correct in saying that galaxy formation involves increasing the density; not decreasing it; but I'm looking for a phenomenon sufficient to reverse the Hubble flow, and clump, surrounded by a homogeneous distribution of matter. In your model, you have the distribution already starting out pre-clumped, and it becomes more clumped.
(3) I don't have any additional evidence. You're already aware of spiral galaxies, bar galaxies, Hubble's law, and globular clusters.

The only thing we disagree about is the level of clumpiness in the universe. You think that the universe is clumpy on the scale of galaxies, and clumpy on the scale of solar systems. I think that the universe is homogeneous on every scale right down to the cubic meter, but clumps up on the scale of stars, because of perturbations.

FYI, I'm going to put on my boxing gloves. If you want to propose a serious astrophysical model, then that means that you want to get into the boxing ring and treated like a professional boxer. So I'm not going to pull punches.

 Quote by JDoolin I don't have a quantitative model, but I can qualitatively describe three distinct stages--perhaps four.
A qualitative model is useless since it's impossible to make predictions that are detailed enough to compare with observations. Now it doesn't have to be a complicated quantitative model, but you need to run some numbers.

One quick thing to calculate is that age of the universe at which the average density of the universe reaches densities that are typical of the interstellar medium. My guess is that it's going to end up before you have any stars at all.

What you need to be able to generate are *NUMBERS*. How many globular clusters do we expect to see? What's the density of galaxies? What's the distribution of bright matter and dark matter? What's the temperature of the gas? I want correlation functions, spectral predictions, etc. etc.

 Extremely high density. Perturbation caused by supernova results in a gravitational gradient sufficient to overcome outward Hubble-velocity.
I don't think this is going to work since you are dealing with different scales. Supernova explosions happen on length scales of kiloparsecs when you already have large local gravitational fields that overwhelm the Hubble flow. If you are talking about supernova shock waves then the Hubble flow is going to be irrelevant.

Supernova bubbles are smaller than galaxies and can't affect Hubble flow. Supernova bubbles also have negligible gravational gradients. The shock wave is purely a gas pressure phenonmenon.

The other thing is were did the supernova come from? If you have supernova then you already have stellar formation, and if you have stellar formation, then things are already clumping.

(2) You are correct in saying that galaxy formation involves increasing the density; not decreasing it; but I'm looking for a phenomenon sufficient to reverse the Hubble flow, and clump, surrounded by a homogeneous distribution of matter. In your model, you have the distribution already starting out pre-clumped, and it becomes more clumped.

Jeans instability.

 The only thing we disagree about is the level of clumpiness in the universe. You think that the universe is clumpy on the scale of galaxies, and clumpy on the scale of solar systems. I think that the universe is homogeneous on every scale right down to the cubic meter, but clumps up on the scale of stars, because of perturbations.
Well, you are wrong.

The matter correlation spectrum is pretty well established, and it pretty clearly shows that things clumped top down rather than bottom up. During the 1980's it was an extremely big debate between the hot dark matter people that argued that galaxies first formed and then clustered into superclusters, and the cold dark matter people that argued that the superclusters formed first.

The data supports the CDM people.

 Blog Entries: 4 Recognitions: Gold Member You bring up a good point. I would be happy to work on this professionally. In many ways it would be a lot easier than what I'm doing now. But right now my time is divided, and this is only a hobby. But regarding pulling your punches, realize that I am skirting the edges of the rules of the forum. I have to be very, very careful what I say, and I may already have said too much. At any time the moderators decide that I am in disagreement with the scientific consensus, or that I'm arguing for a "personal theory," they can delete my post and give me an infraction for my troubles. So you don't have to pull your punches here, but I am not permitted to block your punches in any substantial way, unless I can do it within the context of the standard model. Within those limitations, (with one hand tied behind my back) I have to ask... I presume you mean that the data supported that the matter was cold. The matter was dark. And it was some kind of matter. What was it that convinced them that that cold dark matter was nonbaryonic?

 Quote by JDoolin You bring up a good point. I would be happy to work on this professionally. In many ways it would be a lot easier than what I'm doing now. But right now my time is divided, and this is only a hobby.
This is why "doing science" takes so much time. It's easy for me to come up with new ideas, but to get to the point where I can put that idea in the boxing ring, and not have it get instantly killed takes lots of time and effort.

 At any time the moderators decide that I am in disagreement with the scientific consensus, or that I'm arguing for a "personal theory," they can delete my post and give me an infraction for my troubles.
1) You can step back and ask what *is* the scientific consensus. Asking, so why can't supernova trigger galaxy formation and then listening to the answers is within the rules of the game.

2) The rules are not that it's within the scientific consensus but rather than personal theories are not allowed on the main forums. If you can go into the standard preprint or paper archives, and pull out a paper that defends a theory that's similar to the one that you personally like, then you can discuss that.

There are a ton of papers talking about oddball theories. If you come up with something and it's something that no one has uploaded to Los Alamos, then chances are that it's not really worth discussing.

In the case of galaxy formation there *is* no scientific consensus.

 I presume you mean that the data supported that the matter was cold. The matter was dark. And it was some kind of matter. What was it that convinced them that that cold dark matter was nonbaryonic?
Baryons sound different.

http://en.wikipedia.org/wiki/Baryon_...c_oscillations

Basically baryons will conduct sound waves and non-baryonic material won't. The CMB and location of the galaxies "freezes" the sound waves at the start of the universe, and the fact that baryons will conduct sound and non-baryonic material won't means that you end up with clumps of matter at certain locations.

 One other thing. You'll have to do a bit of digging to find computer simulations of baryon-only universes. They date from the late-1980's when this was still under dispute.
 Here's a graph showing what the universe looks like versus what it would look like with just baryons. http://www.astro.caltech.edu/~george...aa-powspec.pdf It sounds different. If you look at the baryon only graph, you see lots of peaks. Those are standing waves. A baryon-only universe would conduct sound really, really well, so if you imagine a string that goes from one end of the observable universe to the other, and pluck it, you end up with very strong harmonics. We don't see extremely strong harmonics, but we do some some harmonics, which says that the universe is this mixture of stuff that conducts sound very well with stuff that doesn't conduct sound very well.
 Blog Entries: 4 Recognitions: Gold Member (If this is hard to read, I could probably do another Jing video running through it... But maybe you could address any number of items where I appear to be confused. I just picked one of your links http://www.astro.caltech.edu/~george...aa-powspec.pdf and started reading, to the best of my ability; trying to figure out what you're saying.) So for this Power function P(k) is the Fourier transform of the correlation function. xi(r) and w(theta). Now as for spatial and angular correlation functions xi(r) and w(theta), are they looking at r=0 from our position, and theta =0 in some specific direction? Are they using the orientation of our galaxy, or are they using the orientation of the CMBR dipole? However, the article also says dP = nbar^2(1+xi(r12))dV1 dV2 $$dP = \bar n^2(1+\xi(r_{12}))dV_1 dV_2$$ I'd have to review Fourier transformations; Is that an equivalent definition? Now the idea of a Fourier transform, if I'm not mistaken, is to take something from distance or time domain into a frequency domain. It turns a function which is graphed in terms of time or distance into a function which is graphed in terms of frequency, or wave number. The correlation function is xi(r)-the spatial distribution or w(theta)-the angular distribution. Now, “the spatial two-point or autocorrelation function is defined as the excess probability, compared with that expected for random distribution, of finding a pair of galaxies at a separation r12.” By “random” do they mean a “uniform random distribution?” And by “probability of finding a pair of galaxies at a separation r12” are they saying, “Given a galaxy at point 1, what is the probability of finding a galaxy at r2” or are they working from a single origin, and expecting to find galaxies in a more-or-less spherical distribution? Another question--on the correlation function itself. I think of “sound” as a causality relation; not a correlation relation. Is this really a sound wave traveling through the universe now, or is it a correlation function that may or may not be due to a sound wave that went through the universe a long, long, long time ago when the universe was significantly denser? It says that between .1 h-1 and 10 h-1 MegaParsec's the spatial correlation function is well described by a power law (5 h-1/r)^1.8. Unfortunately, the article never tells us what h-1 actually stands for. There's also not really any explanation for where that came from; though it reminds me of an inverse square law that you might get, either from gravitational effects, or intensity effects--anything that is proportional to the surface area of a sphere at a certain distance from an object or event. Also, they quickly change their mind, and decide, instead that xi(r) = 1 over 2 Pi times the integral of dk * k^2 P(k) sin (kr) over kr. $\xi(r) = \frac{1 }{2 \pi} \int{ dk * k^2 P(k) \frac{\sin(kr)}{kr}}$. I gather that is some kind of representation of an inverse Fourier transform, though I don't fully see the resemblance to the Fourier transformations on Wikipedia. It seems like they have k/r sin(kr) but are fixing it up so there's something that looks like the sinc function in there. The article says the paradigm is that “small fluctuations in density are amplified by gravity.” That is a qualitative sort of statement, that could mean just about anything. The main thing I'm questioning is their concept of scale--what is a “small” fluctuation in density if you go back in time to where the mean density of the universe in the first nanosecond? A quantum fluctuation in the first nanosecond or microsecond of the universe will expand over the next 13.7 billion years into the entire visible part of the universe. So yes, essentially that might be what they are saying when they say “one possible explanation being that they are quantum fluctuations boosted to macroscopic scales by INFLATION.” I just don't see why this is in doubt. Given a few carefully chosen, well-reasoned axioms, I would think that this conclusion is virtually inescapable. Now, the primordial power spectrum, assumed to be P(k) proportional k^n, where n=1 is a popular choice... They've defined the Power spectrum so abstractly, I'm not sure which way is up, but is it a useful interpretation to say that this assumption claims that “sound” in the universe is present equally at all wavelengths? I don't think I have this right, but I'm also in great doubt as to the wisdom of transforming the map of the universe from a spatial description to a wave-number description at all. (By the way, on further thinking, I'm not sure the "popular choice" of assuming that P(k) ~ k really makes any sense. Why should there be any a priori assumption about the distribution of wavelengths of perturbations in the universe, and why would it be distributed in this way?) My own feeling is that wave-number-based descriptions of the universe are deeply counter-intuitive. It would be rather like trying to find a Bessel function and Legendre Polynomials to describe the surface of the Earth. Of course, you CAN model the earth this way, but why would you want to? Would it really have any predictive or explanatory power? Could you, from that mapping, then find a useful theory of plate tectonics, volcanism, oceans, etc? A second difficulty I have with what appears to be the Standard Model, and this discussion of “sound” in general, is that to have what we commonly think of as sound, you need to have a region of gas that is more-or-less in the same inertial reference frame, and has a great enough density . It's not a question of whether it happened, but when. It sounds as though most people who support the standard model are under the impression that we should be able to see evidence of sound passing through the universe now. I agree that they should be able to see some evidence of sound passing through the universe long ago. When the universe was one hour old, the particles 1 mile away from each other were moving apart at 1 mile per hour. Yes, in that environment, sound might travel quite well, except for a few caveats. (1) we're talking about a fluid so dense that ANY fluctuation is going to result in massive gravitational instability, and (2) We're talking about a fluid that probably doesn't interact in any way similar to the spring-like molecular interactions we're familiar with. And that region would grow in the next 13.7 billion years to a volume on the scale of galaxies and superclusters. I'm still interested in seeing why they think that Baryonic matter could not have produced what we're seeing, but I think that argument applies only to the early universe when the density was great enough that sound would carry through the plasma. I think there would have been a time in the universe where the density got low enough when baryons would begin to form (then sound would really begin to flow), and then a time in the universe where the density of those baryons got low enough to become almost a vacuum, and sound basically stopped. So if I am understanding properly (a big if, at this point) they think that when Baryons formed, Nuclear interactions start becoming a push/pull interaction rather than just pulling; Hooke's Law would have begun to apply en-masse to all the particles, making the system begin carrying sound. But they see some evidence for sound but not enough evidence for sound, so they decided that most of the mass of the universe is nonbaryonic. You may think I'm trying to construct a straw-man here. If I am, please forgive me. I still mean to just be asking... “What makes you think the dark matter in the universe must be nonbaryonic.” What you've told me is that if it were baryonic, the universe would ring like a bell. What I'm trying to do here is make my best attempt to guess what you mean. I think you must mean that the universe ONCE rang like a bell; when the density was much greater. I'm suggesting that the universe stopped ringing like a bell because it became too diffuse for sound waves to carry through diffuse molecular hydrogen. You seem to be saying that the universe should be ringing still now, except for the presence of nonbaryonic dark matter. Do I have that right?

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 Quote by twofish-quant The rules are not that it's within the scientific consensus but rather than personal theories are not allowed on the main forums. If you can go into the standard preprint or paper archives, and pull out a paper that defends a theory that's similar to the one that you personally like, then you can discuss that.
Not necessarily. What the Rules actually say:
 Quote by Greg Bernhardt Scientific Discussion Guidelines Generally, in the science discussion forums we do not allow the following: Discussion of theories that appear only on personal web sites, self-published books, etc. Challenges to mainstream theories (relativity, the Big Bang, etc.) that go beyond current professional discussion Attempts to promote or resuscitate theories that have been discredited or superseded (e.g. Lorentz ether theory); this does not exclude discussion of those theories in a purely historical context Personal theories or speculations that go beyond or counter to generally-accepted science Mixing science and religion, e.g. using religious doctrines in support of scientific arguments or vice versa. Links to web sites that fall in the categories listed above will be removed. Generally, discussion topics should be traceable to standard textbooks or to peer-reviewed scientific literature. Usually, we accept references from journals that are listed here: http://ip-science.thomsonreuters.com/ Use the search feature to search for journals by words in their titles. If you have problems with the search feature, you can view the entire list here: http://ip-science.thomsonreuters.com....cgi?PC=MASTER In recent years, there has been an increasing number of "fringe" and Internet-only journals that appear to have lax reviewing standards. We do not generally accept references from such journals. Note that some of these fringe journals are listed in Thomson Reuters. Just because a journal is listed in Thomson Reuters does not mean it is acceptable. References that appear only on http://www.arxiv.org/ (which is not peer-reviewed) are subject to review by the Mentors. We recognize that in some fields this is the accepted means of professional communication, but in other fields we prefer to wait until formal publication elsewhere. Physics Forums is not intended as an alternative to the usual professional venues for discussion and review of new ideas, e.g. personal contacts, conferences, and peer review before publication. If you have a new theory or idea, this is not the place to look for feedback on it or help in developing it.

 Quote by JDoolin Now as for spatial and angular correlation functions xi(r) and w(theta), are they looking at r=0 from our position, and theta =0 in some specific direction?
No. What you do is to look at r=0 for some random point in the sky and then calculate the power spectrum with respect to that random point. If the universe is isotropic and homogenous, then you should get the same power spectrum for any random point (and people have checked and we do).

 Given a galaxy at point 1, what is the probability of finding a galaxy at r2” or are they working from a single origin, and expecting to find galaxies in a more-or-less spherical distribution?
If the universe is isotropic then if you start with any random galaxy, you should get the same numbers.

 Is this really a sound wave traveling through the universe now, or is it a correlation function that may or may not be due to a sound wave that went through the universe a long, long, long time ago when the universe was significantly denser?
For CMB baryon oscillations, it's a snapshot of the universe as it was when CMB was emitted. For galaxy counts, the expanding universe ends up "freezing" the sound waves.

 Unfortunately, the article never tells us what h-1 actually stands for.
Hubble's constant. What happens is that when you do the calculation, everything scales to the hubble constant, so you can just put at in as a variable, that way you don't have to worry about what it really is.

 The article says the paradigm is that “small fluctuations in density are amplified by gravity.” That is a qualitative sort of statement, that could mean just about anything.
There are two free parameters in LCDM for this. One gives you the size of the initial fluctuation. The other one gives you the steepness of the fluctuations. You can fit that to the data.

 his assumption claims that “sound” in the universe is present equally at all wavelengths? I don't think I have this right, but I'm also in great doubt as to the wisdom of transforming the map of the universe from a spatial description to a wave-number description at all.
It's just math. You have a differerntial equation in space. You can do a coordinate transform to do the math in wavelengths.

 (By the way, on further thinking, I'm not sure the "popular choice" of assuming that P(k) ~ k really makes any sense. Why should there be any a priori assumption about the distribution of wavelengths of perturbations in the universe, and why would it be distributed in this way?)
That's where inflation comes in......

Inflation says that the universe underwent a period in which it was expanding exponentially exp(ax). So if you have random gaussian flucutations at quantum scales, and you ask what that does to the total spectrum, you get a power law spectrum.

This is why doing the numbers is important. Inflation is more than merely saying that the universe expanded, but once you get the exact numbers, you end up with the initial perturbation spectrum.

 My own feeling is that wave-number-based descriptions of the universe are deeply counter-intuitive. It would be rather like trying to find a Bessel function and Legendre Polynomials to describe the surface of the Earth. Of course, you CAN model the earth this way, but why would you want to? Would it really have any predictive or explanatory power?
Yes, it shows that the universe isn't all baryons, and that baryons cause peaks.

 When the universe was one hour old, the particles 1 mile away from each other were moving apart at 1 mile per hour. Yes, in that environment, sound might travel quite well, except for a few caveats. (1) we're talking about a fluid so dense that ANY fluctuation is going to result in massive gravitational instability, and (2) We're talking about a fluid that probably doesn't interact in any way similar to the spring-like molecular interactions we're familiar with.
1) This isn't true. There is a well known criterion for when something will undergo gravitational instability called the Jeans instability. What you basically do is to calculate the speed of sound in a gas, and if the sound waves spread out the gas faster than gravity can compress it, there is no instability.

2) Fluids are fluids. One thing that happens with the big bang is that the densities pretty quickly go down to the level of things that we run into in daily life. One hour after the big bang, you have a gas of hydrogen/helium at conditions we can simulate with earth based experiments.

 What you've told me is that if it were baryonic, the universe would ring like a bell. What I'm trying to do here is make my best attempt to guess what you mean. I think you must mean that the universe ONCE rang like a bell; when the density was much greater. I'm suggesting that the universe stopped ringing like a bell because it became too diffuse for sound waves to carry through diffuse molecular hydrogen.
We are looking at a snapshot of what the universe looked like at the time the CMB was emitted and the galaxies first formed. At that point the pressure waves got "frozen" which gives us what we see today.

 You seem to be saying that the universe should be ringing still now, except for the presence of nonbaryonic dark matter. Do I have that right?
No. What I'm saying is that observations of CMB and galaxy counts show what the universe was like at the time CMB got emitted and the galaxies started to form. That gives us a snapshot of the that moment, which is inconsistent with all baryons.

Now you could argue that there is some process that converts non-baryonic matter to baryonic matter, but then you look at the list of possible particle physics processes, and none of them fit. If you were arguing for a dark matter->baryon process happening at 10^-2 seconds after the BB, that would be easy. But we are now BB+300,000 years, you have hydrogen gas at 3000K, so if there were some dark matter->baryon conversion process, you should be able to see it in action on earth.

 Blog Entries: 4 Recognitions: Gold Member What is the standard model regarding Hubble's constant? Is it a true constant; i.e. it does not change over time, or is it changing? Is it the reciprocal to the age of the universe, or is it regarded to be an unchanging parameter? Never mind, I think I found it on Wikipedia: http://en.wikipedia.org/wiki/Hubble'...f_the_universe And a little calculation. If q were zero, and the integration constant is zero, then it is the reciprocal to the age of the universe. Attached Thumbnails
 One of way of thinking of the standard model is that it's like piece of software. Cosmological Model 2012 is going to be different from Cosmological Model 1995 in the same way that Windows 8 is different from Windows 95 or Linux 3.4 is different from Linux 1.5. As time passes, people will put in more bug fixes and features, and rip out old obsolete stuff. Right now the big work in Standard Model 2012 involves adding in a galaxy formation model and an inflation model. The perturbation model for the standard model is linear. What that means is that you do a Fourier transform of the perturbations and then assume that the interaction between the wavelengths is small enough to ignore. Once you have galaxies forming, things will definitively "go non-linear" and things will break.

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 Quote by twofish-quant One hour after the big bang, you have a gas of hydrogen/helium at conditions we can simulate with earth based experiments.

From what I understand, we believe that hydrogen and helium first formed at 30,000 years after the Big Bang. By my calculation ,

1 mile/hour * 13.7 billion years = 20 light-years

at one hour after the Big bang, there would have been all the matter now distributed in the nearest 20 light years (the mass of the nearest 20 or 30 solar systems) compressed into the space of a radius of one mile.

This would be like neutron-star like density. I don't think that matter at those densities can be simulated in a laboratory.

 Quote by JDoolin From what I understand, we believe that hydrogen and helium first formed at 30,000 years after the Big Bang.

No. Hydrogen and helium first formed at three minutes after the BB.

At 34 minutes after time zero, the density of the universe was 10 times the density of water....

http://hyperphysics.phy-astr.gsu.edu...tro/bbang.html

 there would have been all the matter now distributed in the nearest 20 light years compressed into the space of a radius of one mile.
There's something wrong in that calculation.

 This would be like neutron-star like density, prevented from collapse only by the fact that there was no gravitational gradient--no net direction of gravitational pull. I don't think that matter at those densities can be simulated in a laboratory.
At three minutes after BB, we are at densities which we can simulate (albeit briefly) on the earth, and it's typical of the densities you find in the sun.

https://lasers.llnl.gov/programs/nic/icf/

Also, we can generate these sorts of temperatures/pressures in hydrogen bombs.

 Blog Entries: 4 Recognitions: Gold Member $$\frac{1 mile}{1 hour}* \left (13.7\times 10^9 years \right )*\frac{8760 hours}{year}*\frac{1 light-year}{5.8785\times10^{12} miles}=20.4 ly$$ I have checked the math now about ten times. Please check, and see if you see an error in the calculation.
 You might start out by explaining how you are setting up the calculation. Where did you get one mile/hour and why are you multiplying it by the age of the universe. Most calculations start with a(t), which is the relative size of the universe. You put in gravity and pressure and then you come up with an equation for a(t). In some limits you end up with some proportions that you can use for quick calculations. Unfortunately, I don't have time to put together a set of intro cosmology lecture notes, although since you know basic calculus, you can definitely follow the dervivations of the basic cosmology equations. I'm sure that someone has done it already on the internet.
 Blog Entries: 4 Recognitions: Gold Member Thanks for your reply. I wasn't sure whether you actually saw an error in the calculation or you were disagreeing with my underlying assumption that the bulk matter of the universe is spreading out at constant speed. I felt that I had justified that assumption in post #28; and thought that I was staying within the Standard Model. I now wonder whether the equation given here $$q=-\left ( 1+\frac{\dot H}{H} \right )$$ is fully compatible with the equation given here: $$H=\frac{\dot a(t)}{a(t)}$$ There are basically two ways of looking at things. One is to expect that there would be a natural relationship between the velocities of distant objects, and their distance, which derives from the fact that they all originated at roughly the same place at the same time. That is essentially the meaning of the first equation. Then there is another way of looking at things; to assume that things did NOT start out at the same place, but did start out at the same time, and that the natural relationship between redshifts and distance has to do with the scale factor, a(t) changing over time, and that is essentially the meaning of the second equation. My calculation of 1 mile per hour times 13.7 billion years was coming from the first assumption, and I gather than Weinberg's calculation of a density 100 times greater than water after 3 minutes was coming from the second assumption. I'll run out to the library, soon, and check out "The First Three Minutes" and see if I can find out why Mr. Weinberg's thought that the early density of the universe was so low. To me, it appears that there are two different models for the universe, both actively in use by the astronomical community, as are summarized here: http://en.wikipedia.org/wiki/Redshift#Redshift_formulae One is for Minkowski spacetime, and the other is for the FLRW metric, and it refers to the cosmological scale factor. In my own reading, the reasoning behind gravitational redshift and velocity-based redshift is made fairly clear, and based on empirical data, and strong reasoning. Whereas the reasoning behind the FLRW metric generally begins with some hand-waving rationale based on a need for greater flexibility, like "What if the universe were spinning?" or "You can't have an expanding isotropic distribution that satisfies the cosmological principle." I know in particular, since you quoted Weinberg, that he uses that latter argument in "The First Three Minutes" and he notably fails to apply the relativity of simultaneity. He makes some flawed argument about the density at point B as seen from A, versus the Density at point A as seen from B. I forget what figure it was in the book... I remember thinking to myself, there must be more than just this one mistake in the book. I remember thinking at the time that I should really work my way through it, find a big collection of errors in Weinberg and others. The problem was that most of the book was much more hand-wavy than that diagram. So really, that one diagram, and his failure to apply the relativity of simultaneity--that was the only real error I saw in the whole book. Even so, if you want to quote Weinberg, it gives me the opportunity to mention that mistake. It is just one mistake, but I remember some quote from Einstein, when a whole lot of people were criticizing his theory, and pointing out lots and lots of mistakes. You don't need lots and lots of mistakes--you just need one. If Weinberg's whole theory is based on his neglect of applying the relativity of simultaneity, then of course the whole theory falls. The only time you can really find an error in someone's reasoning is if they make their reasoning clear. And Weinberg made very clear that he was treating distant events as simultaneous in reference frames that are traveling away from each other at relativistic speeds. Kudos to Weinberg here, though. It's incredibly rare for any proponent of the Standard Model to make their reasoning clear enough that you can find a flaw in it (or to be convinced by it, for that matter). Usually it's incredibly vague reasoning followed by page after page of dense tensor mathematics.