When Will the Big Crunch Happen According to Current Models?

[Jorrie]

I think the result will be a non-linear combination of gravity and a little bit of expansion, but the effect will not be zero.

But I do not think there is 'expansion' per se inside the gravitationally bound structures - just a small constant effect of the cosmological constant that subtracts from the overall binding effect of gravity. Hence slightly larger orbits, but not 'expanding' orbits caused by cosmic expansion. Or do I have it wrong?

I read something along these lines in Carrera and Giulini, http://arxiv.org/abs/gr-qc/0602098

 

[Mordred]

Thats a good article. I've never seen any research to suggest expansion inside gravitationally bound regions other than orbital effects.

 

[Jorrie]

I read something along these lines in Carrera and Giulini, http://arxiv.org/abs/gr-qc/0602098

According to their eq. 86, appendix A.1, the approximate dynamic effect of cosmic expansion $\ddot{r}=\frac{\ddot{a}}{a}r$ depends on the acceleration and not on the rate of expansion. So in early times (decelerating expansion), the dynamic effect on structures would have been in the direction to the structure center, like gravity, i.e. marginally assisting clustering. During the second half of cosmic history it must have been against gravity, gradually growing to a constant positive value in the future.

If taken at face value, $\ddot{r}$ must still be marginally increasing today and hence there must be a very small expansion effect on clusters (or at least on superclusters) going on. Only of academic interest, I guess.