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Dark energy is suggested to be a repulsive force in the universe causing an accelerated expansion. If the amount of mass outside our observable universe is greater than inside (higher mass density), would it not cause an accelerated expansion from our viewpoint?

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This has been proposed as a alternative explanation of the accelerated expansion of the universe. Note that this implies that the universe is non-homogenous on the largest scales and that we happen to be near the center of a relatively lower density region of the universe and that we are surrounded by higher density regions. So it requires that we are in a somewhat special position whereas the usual presumption in cosmology is that the universe is isotropic and homogenous on the largest scales.

It is possible that in the future more evidence will tend to either make this hypothesis more or less plausible. For example if it were found that the acceleration was measurably different in different directions, it would support this hypothesis.

Note, however, that the CMB measurements also support the hypothesis of dark energy. So some other explanation for the CMB measurements would need to be found. The CMB also is strong evidence that the universe is isotropic which decreases the chance that it is non-homogenous.

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This is impossible, because stuff outside the cosmological horizon cannot gravitate on us. The same mistake appears in many papers. –  Ron Maimon Oct 10 '11 at 4:53
    
The denser regions do not have to be outside of our horizon, they just have to be outside the region that is having an accelerated expansion. The region that is accelerating is only the region near us with a red shift (z) of less than 1 or so. So the dense regions just need to be at a z of greater than 1 and thus they can still be well within our horizon. –  FrankH Oct 10 '11 at 6:23
    
Also @Ron, you are right that the dense region cannot be a spherically symmetric shell. It would have to be inhomogenous which is why I suggested that if the acceleration were found to be different in different directions it would be evidence for this explanation. –  FrankH Oct 10 '11 at 6:28
    
ok--- I stand corrected. But when I read this in the literature, often I don't see the distinction made clearly. The inhomogeneity you would need seems to be excluded by structure formation and CMB, however, but at least it isn't ruled out by general principles of causality. –  Ron Maimon Oct 10 '11 at 6:30
    
@Ron, I absolutely agree with you that the inhomogeneous explanation is very unlikely for lots of reasons... –  FrankH Oct 10 '11 at 6:48
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It is not possible for stuff outside the cosmological horizon to affect stuff inside the cosmological horizon, so this is not a reasonable explanation of acceleration. Further, if there is a uniform density of matter, it does not pull stuff inside out. If the Earth were hollow, an object in the interior of the Earth would not feel a force in any direction.

Despite these well known observations, many people have written papers suggesting that the pull of large amounts of matter beyond the cosmological horizon is responsible for observable effects inside the visible universe. These papers can all be easily dismissed, because GR is predictive within one causal patch.

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Despite the weird downvote, the answer is correct. –  Ron Maimon Oct 10 '11 at 15:48
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No, it's not correct. There are many things outside the visible horizon that affect us. For example, the quantum vacuum, the void with nothing in it that causes dark energy to be sucked outward into it.

Gravity doesn't end at the horizon, the gravity of the entire universe has an effect on us, slowing the expansion.

Also, there are many things we can't see even within the observable universe, like if a meteor or black hole was heading for us at close to the speed of light, we wouldn't see it until we were gone.

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