freyar
Extradimensional Explorer
The maths get complicated rather quickly, and I'm hardly following them, but the contribution that the cosmological constant makes to Einstein's equation of general relativity seems to enter into the equation in a different place than the mass energy tensor. That affects the metric (using, say, the Robertson-Walker line element), and has an effect which is similar to that produced by the mast energy tensor, but still seems to be a different contribution.
Maybe it's the math getting in your way, but the cosmological constant comes into the Einstein equation in precisely the same way as the energy-momentum tensor. It is just another kind of energy (potential), like mass and radiation. That's why it is often called "dark energy." The big question is exactly where that energy comes from or if (big if) the law of gravity is modified (rather than there being extra energy).
Just to skip through some of the other discussion, I don't really think issues of quantum gravity are too relevant to how space expands in the presence of a cosmological constant or other dark energy (though they may be important in understanding why, say, the cosmological constant takes the value it does). The cosmological constant is present in our universe everywhere and shows up in Einstein's equation at each point. In the voids between galaxies, it is the most important type of energy; in galaxies, it is negligible.
I'll nitpick a little. Flat spacetime does not expand. Flat space can expand, which gives spacetime nonzero curvature. And the cosmological constant will certainly contribute to that curvature.The cosmological constant does not directly affect the curvature. It affects the rate of change of expansion - which itself does not necessarily affect the curvature. You can have perfectly flat spacetime expanding at a constant rate, or at an increasing rate, and in both the objects will be moving as if the space is flat! Expanding does not directly imply changing curvature.
But, in any case - bound states do not expand.
So what is your take on systems like our local group of galaxies falling into the Virgo Cluster?