Gravitational Slowing Justified in Flat/Near-Flat Universe

[yogi]

The slowing eras of cosmological expansion are generally justified as being due to gravity. How is gravitational slowing justified in a flat or nearly Flat universe. If the universe were closed or if our Hubble sphere were the complete universe, gravitational slowing is a logical
consequence, If one takes the Hubble sphere as a sample volume of a larger universe, the inward gravitational acceleration at the Hubble scale is approximately c^2/R. So one might reason that a mass at the distance of the Hubble scale would be subjected to a deceleration in the range of c^2/R. But that ignores the gravitational pull of the Hubble sphere that has its center on the same line of action at a distance of 2R.

 

[DEvens]

You need to get the cosmological equations from your gravity theory. The only texts I know that do this are _Gravitation_ by Misner, Thorne, and Wheeler, and _Gravitation and Cosmology_ by Weinberg.

 

[PeterDonis]

How is gravitational slowing justified in a flat or nearly Flat universe.

The universe, meaning spacetime, is not flat. Spacelike slices of constant "comoving" time are flat, but that's not the same thing. The curvature of spacetime is what is linked to gravity.

 

[yogi]

You need to get the cosmological equations from your gravity theory. The only texts I know that do this are _Gravitation_ by Misner, Thorne, and Wheeler, and _Gravitation and Cosmology_ by Weinberg.

I have Misner, Thorne and Wheeler. Can you direct to a particular page or section where this issue is treated.

 

[DEvens]

I have Misner, Thorne and Wheeler. Can you direct to a particular page or section where this issue is treated.

My copy is at home. I think it is called "mix master universe" or something like that. The more formal term is Friedman-Robertson-Walker, I think.

https://en.wikipedia.org/wiki/Friedmann–Lemaître–Robertson–Walker_metric

You want to look for the Einstein equations cast in terms of a spatially uniform density system. Compared to some of the other calculations, expansion come out pretty easily.

PeterDonis had the right idea. It's due to the fact that the universe is 4-D, and only uniform in the three space coordinates.

 

[yogi]

The universe, meaning spacetime, is not flat. Spacelike slices of constant "comoving" time are flat, but that's not the same thing. The curvature of spacetime is what is linked to gravity.

Hi Peter

Lets take a very large or infinite universe - gravitational attraction would appear to be equalized in all directions.

 

[yogi]

PeterDonis had the right idea. It's due to the fact that the universe is 4-D, and only uniform in the three space coordinates.

Let me embellish upon your response with simple analogy. If space is modeled as a two sphere with one dimension suppressed, then would the interior rate of time passage be different than the exterior rate? If so could that be an unbalancing cause? I am not sure the analogy is appropriate, and in any event it would not work in a infinite universe. Your thoughts

 

[DEvens]

Let me embellish upon your response with simple analogy. If space is modeled as a two sphere with one dimension suppressed, then would the interior rate of time passage be different than the exterior rate? If so could that be an unbalancing cause? I am not sure the analogy is appropriate, and in any event it would not work in a infinite universe. Your thoughts

You have to be a bit cautious with motivational analogies of this kind. The GR equations change nature pretty drastically when you drop a dimension. And you will also be getting some misdirection out of thinking of cosmological expansion in terms of attraction or repulsion. It's not really like that.

Do the reading in MTW and see if that does not help.

 

[PeterDonis]

I think it is called "mix master universe" or something like that. The more formal term is Friedman-Robertson-Walker, I think.

Those are two different models. The FRW model is the one that is used in cosmology to describe the universe. The mixmaster universe is a speculation about chaotic initial conditions that eventually smooth out and become something like an FRW model, but AFAIK it is not currently used in cosmology.

 

[PeterDonis]

Lets take a very large or infinite universe - gravitational attraction would appear to be equalized in all directions.

Gravity is not a force in GR, and you cannot figure out the dynamics of the universe by looking at "gravitational attraction" in this way. You have to solve the Einstein Field Equations with an appropriate stress-energy tensor. When you do that for the universe as a whole, you get the FRW model that DEvens linked to. That model predicts that the expansion rate of a matter-dominated universe will slow down.

 

[Simon Bridge]

When you say something like this:

The slowing eras of cosmological expansion are generally justified as being due to gravity.

... you are making a mistake. This is the pop-science description... in GR "gravity" is a geometric effect, so, at best, it is saying that the slowing is due to geometry; kinda begging the question.

A more proper statement would be that the slow-down emerges as a result of the application of the Einstein equations with the a particular choice for a stress-energy tensor. To see how this comes about, you need to look more closely at the maths.

When you make observations like:

But that ignores the gravitational pull of the Hubble sphere that has its center on the same line of action at a distance of 2R.
...
Lets take a very large or infinite universe - gravitational attraction would appear to be equalized in all directions.

... basically, you are observing that the slow-down explanation in terms of gravity does not make more than superficial sense in Newtonian terms. You are correct. Well done.