This is not quite what you are wondering. You might find it interesting anyway.
"Dirac proposed that the universal gravitational constant G, is related to the age of the universe."http://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis
I googled it but I don't quite get the idea. Is it that the overall mass of the universe is decreasing as it ages, so there is an average level of gravity that would be decreasing as well?
I have been thinking about the quality of spacetime between stars or between galaxies, but it is not really related to this thread. In this thread I was thinking more about the possibility that the Earth is condensing as it settles and expels energy and gases. This is why I thought prehistoric sea-level might be at a much higher altitude than it currently is.
The thing I wonder about with the spacetime between stars and between galaxies is whether it continues to dilate until it reaches a "plateau" or whether there might be areas of deep space where it actually contracts again for some reason. Actually, the reason is not "for some reason." It is related to my (crankish) idea that the energy emitted by stars may actually propel them higher in the spacetime topography.
Typically I would think of spacetime as a fabric dented with gravity wells of stars, planets, black holes, galaxies, etc. But because I've had this idea that energy counteracts gravitation, it seems like the gravity wells of the stars could be like craters at the top of a mountain/volcano, figuratively in terms of spacetime topography, I mean. This doesn't really make any sense unless there is some mass creating the "valley" that deep space would be, but maybe there is some base-level of spacetime dilation/contraction/density external to that created by mass.
I suppose the best way to describe this idea would be that spacetime fabric would be elastic and tend to contract in the absence of energy to expand it. So the relatively dilated spacetime surrounding a star would be the product of the stars energy output, and as that energy dissipates at farther distances from the star, spacetime itself would tend to re-contract to its baseline density, which I guess would be like how it was prior to the big bang.
This is extreme crank speculation, but it would somewhat explain the appearance of an expanding universe in that light would be slowing down in the contracted spacetime, or put another way, light would have a long path to follow down and back up the deepening valleys in the spacetime topography. In fact, gravity itself might be nothing more than the tendency for spacetime to contract in the absence of energy, which dilates or expands it.
Hopefully I won't get ridiculed to badly for continuing to explore my crank ideas, but I at least feel like mentioning it since it seems somewhat related to this idea of a gravitational constant of the universe.