Easier I think, to write the equations like this, as ASCII allows, see a real picture on the Wikipedia page:

R(ab) - (1/2)Rg(ab) + Lg(ab) = 8*pi*T(ab)

Now, R(ab) is the Ricci tensor, and describes the curvature of space time. R is a Ricci scalar, which also describes curvature. g(ab) is a metric tensor, which describes the geometry of space time. L is the cosmological constant, inserted later by Einstein to prevent the universe from collapsing, since it was thought to be static at the time. This takes care of everything on the left side of the equation. Notice that it's all geometry & curvature, nothing else.

On the right side, we have only T(ab), the stress-energy tensor (which is also called the energy-momentum tensor). Everything having to do with mass, matter, or energy in any form goes here, inside T(ab).

The expansion of the universe can be more easily seen here as generally a result of stuff that happens on the left side, where matter & energy are irrelevant. That's where the cosmological constant is. The original expansion of the universe is a property of R(ab) (from which R is derived), or g(ab). This implies that the addition of matter or energy is not responsible. One hypothesis for explaining the accelerated expansion of the universe is to blame it on the cosmological constant, which becomes more effective, as galaxy clusters get farther apart.

However, since mater & energy & mass are all by themselves on the right side, they too can be responsible for an accelerating expansion (though I suspect not for the original expansion, when there was no matter). Quintessence is an idea based on a scalar field embedded inside T(ab). The cosmological constant is pretty well obliged to be "constant". However, any scalar field in T(ab) need not be constant, and so can create a far mode complicated expansion history. An accelerating universe could, conceivably come to a screeching halt, turn around, and contract, because of the form of the "quintessence field".

In any case, the "mathematical description of empty space" is the left side of the equation