Big Crunch in Robertson-Walker Models

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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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bcrowell
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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).

[...]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.
 

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