Big Crunch/ Big Rip - Eqn of State

[KGC]

Hello, in the eqn of state [density prop. to a^-3(W+1)] if you subbed in W=-2 you get density prop. to a^3. If you then plot a graph of density vs. scale factor it is a straight-forward graph. Good up until then, but then I got the interpretation wrong. This represents the "big rip". But how? I figured that as scale factor goes to infinity then density goes to infinity, an infinite density implied a "big crunch" to me. On further research, it seems the graph was correct, but I interpreted it wrong. Apparently an infinite energy density is needed for the "big rip", but I don't get why this is. How can an "infinite density" tear the universe apart?
Thanks for any help.

 

[George Jones]

Hello, in the eqn of state [density prop. to a^-3(W+1)] if you subbed in W=-2 you get density prop. to a^3. If you then plot a graph of density vs. scale factor it is a straight-forward graph. Good up until then, but then I got the interpretation wrong. This represents the "big rip". But how? I figured that as scale factor goes to infinity then density goes to infinity, an infinite density implied a "big crunch" to me. On further research, it seems the graph was correct, but I interpreted it wrong. Apparently an infinite energy density is needed for the "big rip", but I don't get why this is. How can an "infinite density" tear the universe apart?
Thanks for any help.

This might be a little late to help.

A big rip ocurs when the scale factor a goes to infinity at some *finite* time in the future. To show that this happens in this case, integrate the Friedmann equation to find the scale factor as a function of time.