We calculate a general effective stress-energy tensor induced by cosmological
inhomogeneity in effective theories of gravity where the action is
Taylor-expandable in the Riemann tensor and covariant derivatives of the
Riemann tensor. This is of interest as an effective fluid that might provide an
alternative to the cosmological constant, but it also applies to gravitational
waves. We use an adaptation of Green and Wald's weak-averaging framework, which
averages over perturbations in the field equation where the perturbation length
scales are small compared to the averaging scale. In this adaptation, the
length scale of the effective theory, 1/M, is also taken to be small compared
with the averaging scale. This ensures that the perturbation length scales
remain in fixed proportion to the length scale of the effective theory as the
cosmological averaging scale is taken to be large. We find that backreaction
from higher-derivative terms in the effective action can continue to be
important in the late universe, given a source of sufficiently high-frequency
metric perturbations. This backreaction might also provide a window on exotic
particle physics in the far ultraviolet.Comment: 27 pages, 2 references added, minor clarifications made, comments
added to introduction and discussion, some details moved to appendice
