Could the acceleration of universe expansion be caused by gravity itself? 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?
 A: 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. 
A: 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.
A: 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.
A: The simple answer would be no. If that were the case every thing in the universe would have the exact same gravitational pull. Meaning gravity on the moon, earth and sun would all be the same value and that is simply not the case.
A: I have been working on a similar theory for years, since the type 1a supernova project showed the unexpected acceleration. I tried to publish several times, unsuccessfully. My idea is; yes, it is gravity which causes the expansion because a static universe would be isotropic and homogeneous but a dynamic universe is iotropic but not homogeneous. It is the inhomogeneous distribution of matter (along the observer's line of sight) which drives the expansion.
If so, there would be no need for dark energy. Einstein's lambda would really be zero (he may have been right first time!).
As stated above, this would require another explantion for CMB as a gravitational expansion has no big bang. If the universe is accelerating, all the free charged particles will radiate. Hence: isotropic background radiation. I need to show that it has a 2.7° black body spectrum. That is as far as I have got for the moment on an alternative CMB mechanism.
