# As the universe expands wouldn’t the affect of gravity between large distances decrease and so allow expansion to accelerate?

I have read that gravitation in a homogenous scale of the universe should cause expansion to decelerate. However, that seems to be the opposite of my logical conclusion.

It seems that if spacetime expands then the large scale affect of gravity in that space time volume would be decreased. So stepwise, less gravitational pull would be exerted allowing expansion to increase (or the perception of accelerating expansion).

I would compare this to escape velocity - if something reaches escape velocity - the affect of gravity exerted by those bodies will continually reduce and thus they will accelerate from each other (though admittedly at a lesser and lesser change in acceleration as their distance increases.) [Edit: This part is incorrect as pointed out below]

So why is there a need for dark energy: As everything moves farther apart it, the overall pull would further reduce allowing everything to move apart at an accelerating rate. No need for an exotic dark energy force - just the logical consequence of space time curvature spreading out.

So can anyone explain why it is often stated that “as the universe expands gravity should slow down the expansion.”

Is there something I am missing?

It is not the case that if two objects are moving apart from each other under (Newtonian) gravity that they will ever accelerate away from each other: they will always accelerate towards each other, regardless of whether they are moving at escape velocity. This is easy to see just by considering forces:

$$F = -\frac{G m_1 m_2}{r^2}$$

There is no point where $$F$$ changes sign, and hence there is no point where $$a$$ changes sign since $$a = F/m$$.

That, more, or less, would be the situation for the universe without dark energy (I think you mention dark matter when you mean dark energy as well): the universe would expand but increasingly slowly over time. The expansion might or might not stop, or turn into contraction over time but the time differential of the expansion rate would always be negative.

For that not to be true: for the time differential of the rate of expansion to be positive requires 'dark energy' aka (perhaps) the cosmological constant.

• Oh, yeah I fixed the dark matter. And yes you are right that I made a mistake in the escape velocity. No matter how far apart items are from each other, they will always exert force towards each other - so that analogy doesn’t work. In the large scale with an expanding universe that is another effect that doesn’t apply to the small scale. – Rick Love May 27 '19 at 15:35
• So I am saying that the distance gain of the expanding universe is happening at a velocity greater then the force pull of gravity. So although the gravity does work to reduce that expansion velocity, the additional distance gained in the previous step causes an increasing amount of space to expand which is greater then the gravity deceleration. I.e things are accelerating faster apart because at each step, there is more space between them to expand (which is increasingly greater then the gravity pull). – Rick Love May 27 '19 at 15:51
• Anyway, I think you have corrected my misconception. Gravity should reduce the expansion. – Rick Love May 27 '19 at 15:54