Big Crunch in Robertson-Walker Models

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In summary, in a Robertson-Walker model with a negative cosmological constant, it is possible that the universe will undergo a "big crunch" at a finite time in the future. This would also mean that the scale factor a(t) would be equal to zero at that time. It is worth examining the behavior of the terms in the Friedmann equations to understand how they would evolve. Additionally, in the special case of the Milne universe, the scaling is just a change of coordinates and these two implications may not be equivalent.
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If we were to assume that in a Robertson-Walker model that the cosmological constant was less than zero, would this imply that at a finite time in the future the universe would undergo a "big crunch"? More importantly, would this imply the scale factor a(t) is equal to zero at that time?
 
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Have you tried looking at the behavior of the terms in the Friedmann equations and reasoning about how they would evolve?

The easiest thing to start by doing would be to check whether there is any equilibrium (stable or unstable).

Airsteve0 said:
[...]would this imply that at a finite time in the future the universe would undergo a "big crunch"? More importantly, would this imply the scale factor a(t) is equal to zero at that time?

Why do you say "more importantly?" I think these two things are synonymous, except in the special case of the Milne universe, where the scaling is just a change of coordinates.
 

1. What is the Big Crunch in Robertson-Walker Models?

The Big Crunch is a theoretical cosmological model in which the universe collapses in on itself due to the force of gravity, resulting in a singularity similar to the Big Bang. It is based on the Robertson-Walker metric, which describes the large-scale structure of the universe.

2. How does the Big Crunch differ from the Big Bang?

The Big Crunch is essentially the reverse of the Big Bang. While the Big Bang describes the expansion of the universe from a singularity, the Big Crunch predicts a contraction of the universe back to a singularity. However, recent observational data suggests that the universe is actually expanding at an accelerating rate, making the Big Crunch unlikely.

3. What evidence supports the idea of a Big Crunch?

The primary evidence for the Big Crunch comes from the observed rate of expansion of the universe. If the rate of expansion was slowing down, it would support the idea of a Big Crunch. However, as mentioned before, recent observations suggest that the expansion rate is actually increasing, making the Big Crunch unlikely.

4. Is the Big Crunch considered a viable cosmological model?

No, the Big Crunch is not considered a viable cosmological model due to the aforementioned evidence against it. Additionally, the Big Crunch would violate the second law of thermodynamics, which states that entropy (or disorder) in a closed system can never decrease over time. The Big Crunch would result in a highly ordered singularity, contradicting this law.

5. What are some alternative theories to the Big Crunch?

Some alternative theories to the Big Crunch include the Big Freeze, in which the universe continues to expand indefinitely until all matter and energy dissipates, and the Big Rip, in which the expansion of the universe accelerates to the point where it tears apart all matter, including atoms. Another theory is the Steady State model, which proposes that the universe has always existed in a constant state of matter and energy production, with no beginning or end.

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