# Is the acceleration of the expansion of the universe caused by expansion of spacetime itself?

When considering the accelerating expansion of the universe, it is often stated that dark energy is required to cause acceleration of expansion in order to overcome the pull of gravity.

However, it seems that if the rate of expansion is great enough, this would overcome the effect of gravity that is causing deceleration.

In other words, the distance gain of the expanding universe is happening at a rate greater than the force pull of gravity. So although gravity does work to reduce the expansion velocity, the additional distance gained causes an increasing amount of space to expand. I.e. things are accelerating faster apart because at each step, there is more space between them to expand (which is increasingly greater than the gravity pull).

Let me try to define this better:

Given two bodies in the universe very far apart a,b.

vel_expand - the rate at which the distance between a,b is increasing due to the expansion of spacetime between them

acc_from_expand - the increase of vel_expand caused because of the greater distance between a,b

So as a,b move apart, the space between them increases (which is an increase in the amount of expanding space time between them), which causes a greater increase due to expansion of space time - i.e. an acceleration of expansion due to the expansion itself.

Now on the opposite side of the equation is the pull of gravity (the curvature of space time) caused by the mass of a,b. However, gravity decreases at an inverse square to the distance so it quickly becomes smaller as distance changes.

So as distances become large between a,b there is a point where the acceleration due to expansion of spacetime between a,b is greater than the deceleration due to gravity between them.

So at that point they will continue to expand apart at an accelerating rate.

(This concept is similar to the edge of the observable universe. The distance from which speed of light can overcome the expansion of the universe.)

Maybe this is all completely wrong. But I would like any feedback on whether this makes any sense.

Also in my description, the acceleration of expansion would be a function of the distance between objects - so the further apart 2 bodies in the universe, the faster they would be accelerating apart. I don’t know if that matches measurements - but I have read that there are discrepancies between the rate of expansion measured in the background radiation versus white dwarves vs supernovas.

Does my concept make sense?

If so, is there an article that discusses the acceleration of the expansion of the universe due to the expansion of the universe itself?

If not, where am I wrong in my concept?

• Also, is the the space time constant that Einstein added to the general theory of relativity? (Which in my description is the concept that space time itself expands at a fixed rate)? – Rick Love May 27 '19 at 20:01
• I don't know if this is helpful, but I didn't get "an acceleration of expansion due to the expansion itself". First of all, it should be clarified that expansion of space is expansion of universe (i.e. it's not like the universe is expanding within space, but I somehow think that you already know this). Do you mean that the cause of expansion lies within spacetime itself, so more expansion will lead to even more expansion? – Helen May 27 '19 at 22:38
• If the latter is the intended meaning, then it could have to do with one of the proposed causes of the expansion, i.e. vacuum energy. Also, let's add as was also noted in the answer that objects further apart will not accelerate away from each other more. – Helen May 27 '19 at 22:41
• @RickLove why the deselection? – Árpád Szendrei May 28 '19 at 4:48

You are correct, space itself is expanding, but only in the intergalactic viods of space.

Inside galaxies, space is not expanding, because gravity dominates.

We cannot say that two solar systems in the Milky Way would recede because of space expansion between them.

Space is expanding between the galaxies, where gravity is not dominant, but dark energy is dominant.

The problem lies in the definition of distance (or speed of recession) in GR at an intergalactic scale. There is no such definition of distance (or speed of recession).

It is very hard to define at what rate two galaxies are recessing, and we have no experimental evidence on the expansion of space itself.

So you are saying that if two galaxies are farther apart, they will be accelerating faster then two galaxies that are closer. This is not correct to say. Over large distances, the universe expands uniformly. Though, what you are saying might be right if you say that inside galaxy clusters, space is expanding slower (because of gravity) then in the voids of galaxy groups, space is expanding faster (because gravity has even less influence there).

• I would clarify that if expansion is uniform across the universe, it still occurs in areas of larger gravity, it is simply negligible compared to gravity. Also, I would question whether expansion is uniform across the universe or if there are factors not considered that could be affecting it. – Rick Love May 28 '19 at 3:28

No, the accelerated expansion of the universe is caused by cosmological constant. The cc has negative pressure $$p$$. You may have a look at the Friedmann acceleration equation whereby the term $$-(\rho + 3p)$$ is decisive. The universe expands accelerated if this term is positive which requires that the matter density $$\rho$$ is dominated by the cosmological constant (notice $$p$$ is negative).

Second, spacetime doesn't expand. Note that space doesn't expand by itself. Instead "expansion of the universe" means increasing distances between comoving objects. Whether the notions space expands or distant galaxies are moving away from each other depends on the chosen coordinates. So neither of these views - being not invariant - may be considered as a measurable physical phenomenon. Space expands in FRW-coordinates and galaxies move away in normal-coordinates.