# How could gravity affect the expansion of the universe?

I've read several books which talk about gravity slowing down, halting, or reversing the expansion of the universe. The expansion is often compared to a stretching of space at every point, so that the distance between things is getting larger. Gravity is often described as a distortion of space - I've never heard that it 'stretches', but neither have I heard that it 'pulls'.

So you have a gravitating object like a Sun or a black hole, distorting the space around it. Somewhere else you have another gravitating object, distorting the space around it. On the whole, you have every cubic centimeter of space expanding.

How do the respective local distortions of space caused by the objects slow down the expansion of the space between them? Wouldn't any distortion just contribute to the stretching?

Note: There's another question here: Does gravity slow the expansion of the universe? that has a similar title, but I don't think it addresses what I'm asking.

Also, I am a layman, and I suck at math. I get all my info from popular science writers (Brian Greene, etc.).

• The expansion of spacetime is a large scale phenomenon that operates at the length scales of galaxy superclusters. On the scale of individual stars the gravitational fields of the individual stars completely overwhelm the global expansion of spacetime. The uniform expnsion requires a constant matter density, and it's only at these scales that the averaged out variations in density become small. – John Rennie Dec 29 '14 at 17:22
• Yes but at any scale, gravity works to distort space locally; I don't see how the expansion of the entire universe could be slowed by local distortions. Like a bread loaf, as it bakes, the entire thing expands; the seeds/grains in it may exert pull locally - even whole regions of the interior (clumps of seeds), but how could they negatively affect the entire expansion? – Superstringcheese Dec 29 '14 at 17:47
• Let's suppose stars are roughly equally spread. At any length scale $\ell$ the gravity of any individual star falls as $1/\ell^2$, but the number of stars in a volume of diameter $\ell$ rises as $\ell^3$. So the gravitational force due to a collection of stars of size $\ell$ increases roughly linearly with $\ell$. Now stars are obviously not equally spread out, but the point remains that on large scales gravity becomes more and more important. The gravitational effect of stars is not just local. – John Rennie Dec 30 '14 at 6:33
• I get that. My point is that it seems like all the distortion would just add up to more stretching, not contraction. No post or comment has addressed this point so far, so I'll assume my question just doesn't make any sense. Thanks for your input though. – Superstringcheese Dec 30 '14 at 14:18
• This will rapidly get mathematical, which you wanted to avoid, but a single star doesn't expand or contract spacetime. Technically its Ricci curvature is zero. However a homogenous and isotropic distribution of matter has a non-zero Ricci tensor and does expand or (in a closed universe) contract spacetime. I'm afraid I struggle to explain this in intuitive terms. – John Rennie Dec 30 '14 at 14:50

The answer to your question depends on what we mean by "gravity". When Einstein came up with his field equations, which are the core of general relativity, he encountered a number of possible mathematical choices that one can make with regards to their form.

One of those choices is the inclusion of the cosmological constant. Without the knowledge of precision cosmology data that constant is not actually motivated by physics. Just looking at the set of effects of Newtonian gravity and post-Newtonian gravity (like the perihelion shift of Mercury) that Einstein actually knew about, this constant is either not needed or should be set to zero. Einstein included it anyway because it is required to produce a cosmological solution that is static and he liked the idea of a static, eternal universe, even though no such observational information was available to him. He made a personal philosophical choice, if you like.

Unfortunately for him the Hubble expansion of the universe was discovered soon thereafter, rendering the original need for that constant unnecessary. Einstein called this "his greatest blunder". In a complete reversal of fortunes more precise measurements than those of Hubble and other early precision cosmologists have now turned up an acceleration in the expansion of the universe, which, in the language of general relativity requires the cosmological constant once again! In short, Einstein blundered more when he said that he should have excluded it than when he put it in!

And here is the big question: is "gravity" what we see acting on the short distance scales of planets and solar system and galaxies (requiring no cosmological constant), or is gravity what is obviously acting on the whole universe? If we agree to the latter, and if we take general relativity very seriously (which I personally have decided to do at this level of physical description), then the cosmological constant is part of a consistent description of "gravity". We can't see it on small scales because it is too weak, but on large scales it actually dominates the dynamic and it makes the universe expand ever faster, at least for the time being.

Now, one can take the approach that "gravity" is one force and the cosmological constant is another for which we simply haven't found the proper dynamic equations, yet. In that case it would be nothing but a mathematical accident in the theory of general relativity: nature fooled us again by allowing us to fudge a non-gravitational interaction into the equations of gravity.

That question is, for the time being, not decidable. You can take the side of "gravity" being "ordinary gravity plus the cosmological constant" or you can assume that it's just a fudge. It's a matter of taste, really.

• Thanks for the background, but I'm familiar with the nature and history of the constant. I'm asking how a distortion of space (gravity, at whatever scale) could hinder another distortion of space (the expansion, at whatever scale). Why don't they add up to more expansion? – Superstringcheese Dec 29 '14 at 17:43
• I was responding to your implicit assumption that gravity is one thing, when the equations describing gravity clearly says that it's another. It's not a question of history, even though I tried to make it easier to grasp by presenting the historical development. The question is "What is gravity, does it include the cosmological constant, or not?". If it does, your question is baseless. We simply have to accept that gravity is more than just the geometric description of Newtonian-ish gravity. Otherwise we have to search for a fifth force. Either way we have an equation that fits the data. – CuriousOne Dec 29 '14 at 19:03

The expansion of the universe is characterised by the observation that galaxies with sufficient distance between them are accelerating away from one another.

If a system (i.e. a collection of galaxies, a cluster) is gravitationally bound then it means that the gravity connecting the galaxies within that system is enough to overcome the effects of whatever it is (dark energy) that normally makes galaxies accelerate away from one another.

In this sense, there is always a tug of war between dark energy and gravity, with dark energy dominating at large distances and gravity dominating at smaller distances.

On the whole, you have every cubic centimeter of space expanding.

You are correct to point out that space is expanding, but the statement above is not completely correct. While space is expanding, it is not necessarily expanding relatively between bound objects. During expansion, the spacetime between the Earth and the Moon is only warped by gravity, not by dark energy (nor does the distance between an electron and a proton).

@CuriousOne has an explanation, but I had this half written (and I think it compliments it) so i'm posting it.