# I What is the acceleration of expanding space?

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1. Dec 19, 2017

### Staff: Mentor

Yes.

The average matter density "has no effect locally" because it has no meaning locally.

Where does this "therefore" come from? Are you assuming that the comoving particles have negligible stress-energy and therefore don't affect the spacetime geometry? If you are, then that makes the particles comoving and not bound gravitationally, yes.

What average matter density are you talking about? And what dynamics are you talking about?

You seem to be confused about how models work. When we talk about the average matter density of the universe as a whole, we do so because we are talking about a model of the universe as a whole. The dynamics of that model, at least to a good approximation, are determined by the average matter density (more precisely the average stress-energy, which might include things other than matter, like radiation or dark energy).

When we talk about a gravitationally bound system, we are talking about a different model with different dynamics, so we have to talk about a different stress-energy: the stress-energy due to the parts of the gravitationally bound system. The average matter density of the entire universe has no meaning in this context. Note, however, that dark energy density still does, because dark energy density really is constant everywhere; it's not an average, it's actually physically constant. That's why we can talk about the (in practice much too small to measure, but present in principle) effect of dark energy on a bound system, whereas it makes no sense to talk about the effect of the average matter density of the universe on a bound system.

In your example here, you appear to be talking about something in between: the dynamics of the super void patch, which is not a bound system but is not the universe as a whole either. If the super void patch really is void, i.e, there is no stress-energy inside it except for dark energy (i.e., the cloud of comoving particles has negligible stress-energy), then it can be treated as a patch of de Sitter spacetime and its dynamics will be the dynamics of such a patch. (This also assumes that the rest of the universe outside the patch is spherically symmetric, as seen from within the patch--that ensures that the spacetime geometry outside the patch has no effect on the geometry inside the patch.)

2. Dec 19, 2017

### timmdeeg

Yes I was assuming this and appreciate that you are precise. This helps a lot.

Saying " because the average matter density has no effect here" I meant it can't be applied here, so it makes no sense to mention it at all. I seem to suffer from incorrect wording.

Ok.

Thank you very much, your answers during this discussion led to new insights and may be more important to correct some wrong notions.

3. Dec 19, 2017

### Staff: Mentor

Ah, ok, yes, that's fine.

4. Dec 19, 2017

### Staff: Mentor

You're welcome!