When Will the Big Crunch Happen According to Current Models?

[Mordred]

Thanks for the link. I'm going to need to examine it in more detail later on. Easter dinner and all with the family

 

[Passionflower]

Well there do exist solutions such as Schwarzschild-deSitter (or just a schwarzschild in a general FRW background) in which you can effectively see the effects of the large-scale expansion of the universe on the local geodesics around the black hole, i.e. on orbits of bodies. Perturbatively, it just shows up as a small extra force which serves to slightly enlarge the orbits.

Indeed.

To me it seems logical that if there is an expansion it must apply to all scales.

 

[Mordred]

Well expansion does apply at all scales. If you were to work out the amount of vacuum or dark energy. You will quickly realize that per cubic meter the amount of energy is extremely small. A rough estimate is 6*10-10. joules sorry for the long hand on my phone atm.

This low energy density is easily countered by gravity. the statement that expansion does not apply in graviationally bound regions is somewhat misleading. The cosmological constant applies everywhere.

however gravity can over power the low energy density of the cosmolical constant.
However in the example above it does have small influences even in gravitationally bound regions.

 

[Passionflower]

the statement that expansion does not apply in graviationally bound regions is somewhat misleading.

I would say it is simply wrong.

however gravity can over power the low energy density of the cosmolical constant.

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.

 

[Mordred]

Correct there is always some influence

 

[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.