# Expansion of space and gravity

In my previous question I asked how gravity can be represented as dents in space. It seems that it's a metaphor. But I wondered with spac expanding does the effect of gravity get bigger as well, I know from other questions that mass doesn't expand like the gaps between mass do although I have no idea why. So using the metaphor from before does the expansion of space cause the "dents"(gravity) to increase?

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The view of spacetime as sliding point of space in a foliation of spatial 3-dim surfaces is helpful. Gravity commoves particles with the sliding of points. In the case of a black hole this commoves particles with points sliding into the black hole.

The de Sitter spacetime is similar to this, but with the flow in the opposite direction, without the singularity and the coordinate dependency with the radius. The cosmological horizon $\Lambda$ determine the Hubble parameter $H~=~ 8\pi G\rho/3$, for $\rho$ the vacuum density of the universe. This determines the cosmological constant as $$\Lambda = (3H^2\Omega/c^2)$$ where we take $\Omega~=~1$. The cosmological constant $\Lambda~\simeq! 10^{54}cm^{-2}$, and the cosmological horizon is at $r~=~\sqrt{3/\Lambda}$ which is at about $10^{10}$ light years. The CMB limit is beyond the cosmological horizon. Multiplying this by the relationship $v~\sim~Hd$ gives $v~=~c$. The cosmological Doppler shift is then at the cosmological horizon $z~=~1$.

There are some departures from this, for the de Sitter metric involves an exponential and there are deviations from $v~=~Hd$ for large enough $d$, but this is close enough. The most distant galaxies observed with z = 7 or 8, these galaxies are being commoved by the expansion of space at about 7 or 8 times the speed of light! The CMB with $z~\sim~ 1000$ is moving out at about that many times the speed of light. This is terribly confusing, and I see professionals, even some rather lionized ones, get tripped up on this. An observer who passes into a black hole has entered a region where they are being dragged by the isometries of space faster than light relative to things outside. Yet this observer will still be able to observe things outside the black hole before they crash into the singularity. What the observer is not able to do is to send a message to things beyond the black hole horizon. The same thing works with the cosmological horizon. We will never be able to send a message to any galaxy beyond it. We can however see everything into the past of the universe as far as our past light cone reaches.

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Well, no. As the universe expands (note this is an intrinsic expansion. Don't think of it as expanding into anything.), the matter and radiation do not increase, and are present in a much larger space. The vacuum energy (cosmological constant) does not change as the space expands--it is the same per unit volume, and its contribution is to exert a negative pressure, a sort of anti-gravity. Note, however, that the pressure contributes to the right side of Einstein's equation--the Stress-Energy Tensor, so it is important dynamically in the evolution of the gravitational potentials( generating the metric) on the left side of the equation. Most models assume the vacuum energy density is constant, but some consider models where it is slowly decaying or slowly increasing. A huge problem is that the predicted value of the cosmological constant (by QFT) is $10^{120}$ times larger than the observed value, a problem that has not been satisfactorily explained.

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Here is an answer on a more metaphorical level: Think of the "expansion of space" as "new space is created out of nowhere".

Do you know the movie "Poltergeist"? There is a scene where the mother runs down the corridor to reach the door to her daughter's room, who is in trouble, but the corridor expands at almost the same speed she is running at, moving the door away from her. (Don't worry, she accelerates, reaches the door and saves her daughter. I think.)

Note that in the case of general relativity, there is no outer space, that is the house is all there is, there is no garden, and if there where, the creation of new space in the corridor does not lead to an expansion of the house that would be observable from the garden.

So, if you replace the door with a star that attracts you (through gravity, not through its beauty), you'll see the star "moving away from you" (only that space is created in between, its not the star that is moving), therefore you'll feel a decrease in the attraction.

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"Poltergeist" meets curved spacetime - that's an excellent tag line for an awesome new movie merging campy horror and hard science fiction. – user346 Mar 27 '11 at 16:06