Gravity of Universe A Million Years Ago: Affect Us?

[OOF]

Choose any distance in the universe, a million light years. This distance creates around us a sphere that divides the universe into three parts. Universe outside the sphere, universe within the sphere and universe on the surface of the sphere.
We are going to determine the gravity of the universe a million years.
1- Outside the sphere, the gravity of a million years ago does not affect us, it is very far away and has not yet arrived.
2- Within the sphere the gravity of a million years ago does not affect us, it has surpassed us.
3- Only the gravity of a million years ago generated by the matter contained in the spherical surface acts on us.
But in this case it is null, in the same way that the gravity of a planet at its center is zero.
Conclusion the gravity of the universe a million years ago does not affect us.
Two million years ago, either.
The one of three million years ago either ...
Agree?

 

[Ibix]

In a homogeneous universe there is no gravitational pull from the universe at large. Locally the universe is not homogeneous, so paths can be curved by variations in matter density such as galaxies, stars, and planets. The million light year scale is well within this range, so the sum of interactions from matter on a surface this small may well not be zero. Also you need to worry about the distribution everywhere along our past lightcone, not just the million year ago bit.

But you can ignore everything outside our past light cone for simulation, yes.

On large enough scales you will need to worry about the curvature of spacetime due to the large scale homogeneity. You then do need to worry about the rest of the universe, but it's all approximately the same so it's not too hard.

I'm not entirely sure if that answers your question.

 

[jbriggs444]

1- Outside the sphere, the gravity of a million years ago does not affect us, it is very far away and has not yet arrived.
2- Within the sphere the gravity of a million years ago does not affect us, it has surpassed us.
3- Only the gravity of a million years ago generated by the matter contained in the spherical surface acts on us.
But in this case it is null, in the same way that the gravity of a planet at its center is zero.
Conclusion the gravity of the universe a million years ago does not affect us.
Two million years ago, either.
The one of three million years ago either ...
Agree?

The only sense I can make of the scenario you propose is if all the matter (and gravity-producing stress and momentum) in the universe snapped into existence a million years ago, existed for a split second and then disappeared. But that scenario is impossible. So what is it that you actually have in mind?

 

[OOF]

"In a homogeneous universe there is no gravitational attraction of the universe in general." I'm staying with this. Thank you very much Ibix.

 

[PeterDonis]

"In a homogeneous universe there is no gravitational attraction of the universe in general." I'm staying with this. Thank you very much Ibix.

You missed a key statement in the latter part of @Ibix's post:

On large enough scales you will need to worry about the curvature of spacetime due to the large scale homogeneity.

In other words, the conclusion you are trying to draw, which is basically that none of the matter in the universe affects us at all, is not correct. The matter in the universe does affect the overall curvature of spacetime, which affects us because it affects how the universe evolves, and we are in the universe.

 

[rootone]

Are you thinking of the Hubble radius?
Beyond this distance no light can ever reach Earth.
It is reasonably assumed that therefore gravity of any such distant object is also zero. as far as the solar system is concerned.

 

[PeterDonis]

Beyond this distance no light can ever reach Earth.
It is reasonably assumed that therefore gravity of any such distant object is also zero.

I don't know how often this is "reasonably assumed", but in any case it's wrong, at least if "gravity" includes the overall spacetime geometry of the universe.

 

[George Jones]

Are you thinking of the Hubble radius?
Beyond this distance no light can ever reach Earth.

This is not correct. Look at Figure 1 from "Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the universe" by Lineweaver and Davis,

https://arxiv.org/abs/astro-ph/0310808

The grey crosshatched region is the region of spacetime that is outside the Hubble radius, and that is or will be causally connected to us. In particular, the past lightcone from our "now" event crosses the Hubble radius.

 

[rootone]

OK thanks for correcting me on that,