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Is the expansion of the universe proof of the Big Bang theory?

Or are there other proofs?

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Whether the big bang is a theory or a model, it cannot be "proved". Scientific models and theories can only be falsified.

I think what you mean is - are there other pieces of evidence that are used to support the big bang model? Or possibly are there other pieces of evidence that support the idea that the universe was once very small and very hot?

The answer is yes. Probably the two most important pieces of evidence are found in the cosmic microwave background and the primordial abundances of deuterium and helium.

Both of these are direct and inevitable consequences of having initial conditions of a very hot ($>10^{10}$ K) and dense universe about 13.8 billion years ago that expanded adiabatically. In particular they both feature evidence that can bee seen in the universe today (the temperature of the CMB and primordial abundances measured from pristine materials or very old stars) that depend on a single free parameter - the photon to baryon ratio. To me, the fact that these very dissimilar phenomena, that are produced when the universe was about $10^{10}$ K and $3000$ K respectively and at densities differing by many orders of magnitude can be simultaneously reproduced is perhaps the biggest success of the model.

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In and of itself, no the expansion of the universe is not proof of the big bang. Other theories could be constructed that would also be explained by the expansion. For example Fred Hoyle and others proposed the Steady State Theory which proposed that new matter was constantly being created thus causing the expansion. A the time there was no other evidence for either theory so either could have been true.

However, when you couple the expansion with other evidence such as the cosmic microwave background radiation discovered in 1964 then it does strengthen the case for the big bang being the cause.

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    $\begingroup$ The ratio of hydrogen to helium in the universe is easy to measure, and is exactly what is predicted by the Big Bang theory. $\endgroup$
    – Marc
    Commented May 23, 2014 at 1:25
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    $\begingroup$ This is just wrong. The Steady State Theory proposed by Hoyle does indeed predict the random creation of matter out of nothing, but not as a means of explaining the expansion. The reason this was put in the theory was to allow for the universe to remain "steady" (e.g., constant density, etc.) throughout it's infinite existence. Obviously if its expanding, it should get less dense meaning it isn't static and Hoyle disliked that so he proposed that matter is constantly created to make it static. He had no explanation for what caused the expansion. $\endgroup$
    – zephyr
    Commented Oct 28, 2016 at 18:01
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No certainly not. This is why Alan Guth and others have not received a Nobel Prize for their inflation theory. Some theories can be quantitatively accurate just by chance. I think that the big bang theory will only be proven when dark energy and dark matter are properly explained and then more incontrovertible predictions can be made.

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Gravity holding our universe together if you look at the universe from outside of the universe you will see avery things all the galaxy avery things in our universe holds together and avery things are moving because of matmtics of universe.

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