Hi,
I had an idea before about how curved space time might have a tendency to expand in order to flatten out to a lower energy state, which could explain the dark energy force, the matter in the curvature would still be gravitationally attracted, but there would also be a repulsive force and a "flow" of spacetime outwards.
I thought of a simple way to measure if this is possible:
Since there is an outward flow of spacetime in curved space, in the solar system the center of curved spacetime, the sun will have an outward flow in all directions, and each planet has its own smaller outward flow in all directions, but the net flow is outwards solar system wide. This effect is small compared to the attractive gravity forces so is mostly unnoticed, but if it exists it should be measureable as a doppler shift in the light coming off masses. Ie. for the earth, there should be a net spacetime flow vector pointing away from the Sun, so the frequency of light emitted from the earth on the sun facing side of the earth should be slightly higher than the frequency of the light emitted from the earth on the other side, since the spacetime flow is equivalent to a movement in spacetime it will produce a doppler shift in light.
Are there any satellites around earth that measure very small doppler shifts like this? I think that would be a good general purpose type measurement.
The doppler shift measurement could also be done between satellite aggregated over orbits.
Also for redshifted galaxies viewed from earth, the dark energy to gravity ratio for the whole mass of galaxies is high enough (gravity is weak) that the galaxies are moving along with the outward spacetime flow, but if they were "stationary" and spacetime was still expanding there should be a blue shift on them when viewed from earth too.
cheers, Jamie