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I reformulate the question a little bit because I feel that I was misunderstood. There are cosmic observations that tell us the universe seems to expand. It also seems to expand always faster (accelerating). I am missing the step of reasoning that, from the collected data, leads to the conclusion that it is certainly expanding. I mean: did they (the astrophysicists) checked that it can't be possible to see an "apparent expansion" even in a collapsing universe, before making their claim? Are there other different (from the redshift) observations that reinforce the conclusion of the expansion? Or: is this theory enough robust today, in order to exclude a possible "revolution" similar to the Ptolemaic/Copernican one (in the near future) ?
Thanks for explanations.

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""What about the statement that if we were involved in a gravitational collapse then the observations will be the same? i.e. apparently expanding"" Who says so? –  Georg Nov 29 '11 at 12:28
@Georg: Perhaps the statement is that the universe is collapsing, but the entropy of the endstate is zero, so that time is ticking backwards? –  Ron Maimon Nov 29 '11 at 18:03
@Ron, such things are discussed for oscillating universes, but not that the contracting univers looks as if it were expanding. –  Georg Nov 29 '11 at 18:07
@Georg: if the universe is contracting to a zero entropy endpoint, you would still call it "expanding". But this is not the question. The question is about tired light. –  Ron Maimon Dec 21 '11 at 19:33
Related: physics.stackexchange.com/q/2110/2451 and links therein. –  Qmechanic May 4 '13 at 18:51
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You are asking: is there any independent evidence, other than redshift, that the universe is expanding. This is a sensible question. In the old days, some people postulated "tired light", the theory that light just gets spontaneousy redshifted with time. This theory is not theoretically compelling, but it does ask that there should be independent evidence that the universe is expanding.

Big Bang nucleosynthesis

If the universe is actually expanding, and its not tired light, then there must have been a time when it was very hot. During this time, the temperature would decay in a very precise way, determined by General Relativity. Alpher and Gamow were able to calculate the amount of each element and isotope produced in this hot phase of the big band, within a few minutes of the birth of the universe.

The results are that 75% of the universe is Hydrogen, 25% is Helium, and a precise calculable trace amount is Deuterium, Lithium, Beryllium, He3. These abundances very across more than 5 orders of magnitude, and they are crazy numbers which are very sensitive to exactly how much matter is in the universe, and the precise masses of the fundamental particles.

These calculations match the observed abundances of H,He, Li, and the trace elements, with tiny residual errors. This is very strong evidence that the universe used to be hot.

Cosmic Microwave background

The Cosmic microwave background is relic radiation from the big bang. Tired light can account for the redhsift, perhaps, but it would not explain why at the edge of the visible universe we see a residual radiation which is at a definite temperature which matches observations.

This is also compelling evidence for the hot big bang. Further, the anisotropies in the microwave background are correctly predicted by inflation, using the observed abundances of normal and dark matter, inferred by other means. The accelerated universe is also in accordance with the cosmological constant required for inflationary theory to match observations. The detailed distribution of the temperature deviations of the microwave background would require an unbelievable conspiracy of tired and conspiratorial light to reproduce.

Structure formation

The theory of the big bang also predicts the formation of large-scale-structure in the universe, which is as expected, with simulations matching observations of the gap-structure and filaments in the large-scale universe, from the initial seed provided by inflation. These predictions are further confirmation of the circle of ideas.

Some of the most obvious signs of a universe expanding from a big-bang is that far away objects are more poorly developed than closer objects.

Is it possible that everything is wrong?

It is not realistically possible that all this is wrong, because the evidence was already too great to deny before the modern revolution in cosmology, and it has gotten much better.

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first of all thank you for your answer. I need to go a little more deep into my argument. Big Bang nucleosynthesis is OK, but it does not prevent that the universe could be, right now, collapsing. The CMB is the relic of Big Gnag, OK, but same as above, I can't see why it would'nt be the same if all is collapsing out there. (I do not know/understand the implications of the anisotropies..). large-scale-structures... same comment. Please help me a little bit more. –  user6090 Dec 6 '11 at 7:30
@user6090: presumably if the universe is collapsing right now, it didn't just suddenly start collapsing just now. The structure formation calculation starts with CMB, and reproduces the rough statistics of galaxy walls and filaments, something which depends sensitively on the expansion over the past 13 billion years. General Relativity plus a small cosmological constant predicts the expansion exactly, so we have a compelling theory which matches observations, and which tells you exactly how the universe expansion goes. Further, this theory matches the redshift data, which you dismissed. –  Ron Maimon Dec 6 '11 at 7:49
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I don't know of the statement claiming similarity between collapse/expansion but theory and experiment tell us that the almost universal red-shift we observe would be a blue shift; If the universe were collapsing.

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