
#73
Dec1007, 05:53 PM

Emeritus
Sci Advisor
PF Gold
P: 2,977

Furthermore, the cosmological principle can be tested empirically within our observable universe. Beyond this, we can't test any theory  for all we know gravity and electromagnetism are completely different outside of our observable universe. Does this mean that the law of gravity cannot be tested empirically? It's not clear to me that you understand the problem fully enough to be reaching such sweeping conclusions. If you're confused about something, please ask. This forum is primarily designed to have experts answer the questions of nonexperts, not for the formulation of personal theories. Please be careful that this does not turn into one. 



#74
Dec1007, 05:55 PM

Astronomy
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PF Gold
P: 22,809

Personally the most authoritative and recent source I know is March 2006 http://arxiv.org/abs/astroph/0603449 Everybody cites itit's the official implications for cosmology part of a multipaper series reporting the 3rd year data from the WMAP satellite. If you look on page 50, caption to figure 17, you see a 68 percent errorbar for Omega which is [1.010, 1.041] The errorbar is based on combined data from four major projects: WMAP CMB, supernova, the Sloan digital sky survey, and the 2degreefield galaxy redshift survey. As of 2006 that was about as good as it gets, and I haven't seen anything since then that is more highly cited. To me that 1.01 is not SURPRISINGLY close to one. Reasons have been offered why, if the universe is spatially S^3, one would nevertheless expect it to be very expanded and so have a small curvatureto be near flat in other words. The errorbar being close to one is not especially remarkable. What is remarkable IMO is that it does not contain oneit is all on the upside. So what [1.010, 1.041] says to me personally is that they already HAVE an errorbar that says S^3, they just don't have enough confidence on it. 68 percent is not enough to disfavor the infinite R^3 case. So I could conclude something if I saw a similar errorbar like [1.010, 1.041] and it had 95 percent confidence. There are technical issues about how you interpret. Like this particular figure assumes dark energy had constant pressure/volume ratio, but they let the constant ratio take on various values. And people can argue should they have allowed timevarying dark energy, or maybe should they have forced the ratio to always be exactly one etc etc. But the technical details don't change the overall sense I get that nowadays the Omega errorbar tends to be mostly over to the > 1 sidesaying "nearly but not exactly" flat. And that the confidence is not high enough to reject the flat case, so one says it is still "consistent with the data" (i.e. flat is not ruled out.) 



#75
Dec1007, 05:58 PM

Sci Advisor
P: 1,253

The point is that if our model describes an infinite Universe, whereas in fact we are in a Universe that is very very big (much bigger than the observable Universe) then the model works perfectly well. If in the future we discovered the Universe was in fact finite, but much much bigger than the observable Universe we would for most cases simply use the infinite model, since the difference between the two is vanishingly small and the calculations are easier in the infinite model. We do things like this all the time, for instance we think General Relativity is the true theory or gravity, however we usually use Newtonian gravity for most things since the Newtonian model is simpler and easier to work with and the two models give the same answer for most questions we have. This is how science works, we seek to find models that match what we observe, described in the simplest way possible, rather than making metaphysical statements about the extent of reality. If the infinite model works we'll use it, it doesn't matter if whether or not the Universe is truly infinite, that's not the point of the assumption or the model. 



#76
Dec1007, 06:08 PM

Sci Advisor
PF Gold
P: 3,273

[tex]a(t) = a(t_0)(\frac{t}{t_0})^{\frac{2}{3}}[/tex] and so as [itex]t \rightarrow \infty[/itex] so [itex]a(t) \rightarrow \infty[/itex]. [itex]\Omega[/itex] > 1. However, with the present understanding of DE the universe will continue to expand, and accelerate in its expansion, even if [itex]\Omega[/itex] > 1. What type of boundary are you thinking of anyway? Garth 



#77
Dec1007, 06:14 PM

P: 119





#78
Dec1007, 06:22 PM

P: 119

Thanks, Garththis is really helpful.




#79
Dec1007, 06:30 PM

Emeritus
Sci Advisor
PF Gold
P: 2,977





#80
Dec1007, 06:40 PM

P: 119





#81
Dec1007, 07:02 PM

Mentor
P: 8,287

Any review papers you can suggest will be appreciated! 



#82
Dec1007, 08:41 PM

P: 34

I am a scientist by trade, so I know how the process works. Discussion here is much more pedagogical, but the basic mode of discourse is the same. If what you have to say is supported by scientific research and/or general knowledge, then say it and present your support. If not, then you can either ask about it or keep it to yourself.[/QUOTE]
AMEN to that! 



#83
Dec1007, 08:57 PM

Emeritus
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PF Gold
P: 2,977

Inflation and Eternal Inflation 



#84
Dec1007, 08:57 PM

P: 34

But The universe has at least 4 dimensions by the most conservative estimate and 11 or 12 dimensions as the normally accepted Number. S or R =3?




#85
Dec1007, 09:15 PM

P: 119

Also, I am not presenting a theory here. This you must understand. I am asking about the justificatory basis of your theory (viz. the infinite Universe). If you have a sound argument, you should be able to present it without difficulty. I'm simply asking for clarification and pointing out lacunae if I see them. It is sometimes good to have a logician looking over your back, don't you think? 



#86
Dec1007, 09:35 PM

Emeritus
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PF Gold
P: 2,977

http://www.physicsforums.com/showpos...3&postcount=61 If you need me to expand or clarify anything, please say so rather than pretending it was never posted. It took several nearly identical explanations of Occam's Razor before you stopped trying to use it in your arguments. 



#87
Dec1007, 09:51 PM

P: 34

I got to go with Space Tiger on this one. I think your questions have been adequately answered several times over. Some very smart people, myself not included, have looked at your problem from several different angles. Cosmology is a not a hard science. There are not a lot of hard facts around to base assumptions on. And we can talk till the cows come home, but if you reject all explainations offered, what are we accomplishing? My experience is more on the nuclear Engineering side, but I try to keep up with what is going on. I will caution you that There is a lot of Pseudo Science running around and I wonder if this where you are coming from. PsudoScience attempts to make the science fit the desired outcome, rather than the other way around. And where the facts don't support the theory, the facts are ignored. There has been a lot of that going around since the Clinton Years. s 



#88
Dec1007, 11:12 PM

P: 119





#89
Dec1007, 11:33 PM

Sci Advisor
P: 1,253

However, neither of the above arguments I just made are reasonable. Clearly we do not have conclusive evidence either way. What we do know is that we have not reason to doubt that the cosmological principle applies for the extent of our observable universe, for this we do have hard evidence such as the isotropy of the CMB (the anisotropies are of course of great interest, but are very small in agreement with the cosmological principle), and the general isotropy of galaxies and QSO's seen in large redshift surveys. Given this data then, we can see that if the Universe is finite, it is clearly at least much bigger than the observable Universe, and for all intents and purposes is infinite. Assuming the Universe is infinite makes the equations easier to deal with, since there are less parameters. I'm not sure how to discussion got to the point of demanding conclusive evidence for the infinite nature of the Universe? Surely this is impossible! We can only ever say that was haven't observed something, we can never have proof that is doesn't exist. To make a whimsical example, it is not reasonable to demand that someone who says that talking monkeys with teapots for hands do not exist provide evidence for their nonexistence. All you can do is point to the evidence that we have not observed such things, and it makes evolution a simpler model if it does not have to explain why monkeys should have evolved teapots in place of their hands. To further the silly analogy, we could make theoretical predictions about the problems monkeys would face with teapot hands, just as we can make predictions about the problems an edge to the Universe would introduce. In both cases our theories may suggest the nonexistence of something but to prove with evidence the nonexistence is clearly impossible. Theories are constructed based upon what is observed, and are made to be as simple as possible given those observations. This is why we assume the Universe is infinite, in full knowledge that this is not absolutely neccessarily the case. 



#90
Dec1107, 12:37 AM

Emeritus
Sci Advisor
P: 7,445

Regardless of whether or not there is an edge to the universe, there is a definite edge to this thread. A rather unpleasant one.
So, let's all try to be nice to one another, and get the thread back on track (as Wallace ha noted, it's started to drift). Otherwise, I'm going to get grumpy and start doing grumpy things.... One thing that pushes my buttons is Ordo's idea that SpaceTiger should have unlimited amounts of time to answer his (Ordo's) questions. In an ideal world, this would be nice, but people have to be able to live with the fact that moderators and mentors may actually have other things in their life other than PF, hard as it may be to believe.... 


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