An interesting paper here to read is by Wiltshire. He makes an argument I compltely agree with that general relativity may not apply for cosmology appropriately. He argues for a cosmological equivalence principle based on conformal theory.
A metric is often modified by some scale factor Q so that g_{ab} ---> Q^2g_{ab}. There there is the issue of what is conformally invariant, which in GR is the Weyl curvature. So for the metric line element
ds^2 = g_{ab}dx^adx^b
for a diagonal system we have that the conformal transformed element is
ds^2 = -Q^2(u)(du^2 - dr^2 - r^2dOmega^2).
Now I write the time part as u, because suppose that Q^{-2) = du/dt, then we can write this as
ds^2 = -dt^2 Q^2(dr^2 r^2dOmega^2),
where for this conformal factor Q^2 = exp(sqrt{L/3}t), (L = CC) this gives the deSitter spacetime. So this time dependent conformal transformation can in a special setting define the deSitter cosmology. So this means that in the cosmology the equivalence principle is extended to frames which are conformal. So the comoving frame, which "surfs" on the expansion (Q-dot/Q)^2 = L/3 = H^2(Omega)/c^2, is in effect on a local inertial frame with the expansionary factor. We might call this a cosmological equivalence principle, which generalizes the notion of how we define frames globally.
There are some subtleties with this, for the Minkowski spacetime has four Killing vectors defined globally (K_i = partial_i) while for cosmologies this is an approximation. Cosmologies as type O Petrov-Pirani solutions have no Killing vectors. This is because different regions have different "time vector fields," for lack of a better term, and how a local inertial frame is defined is now generalized.
If we think in a reciprocal scale, think as a solid state physicist with Briollioun zones etc, then in this inverse space something similar may obtain. In string theory the structure of gravity assumes higher order terms, which suggests that something similar in an inverse setting is taking place. These higher order terms are I think similar to stimulated emission in laser physics, or its classical analogue of a microphone-amplifier feedback.
Now suppose that there is a parameter p associated with the deviation from standard general relativity in cosmology. Similarly suppose there is an order parameter q for deviations from GR in string theory. We might postulate that pq = constant. If I were so bold I might go so far as to say that constant is hbar.
Lawrence B. Crowell