Cosmological back-reaction in modified gravity and its implications for
  dark energy
  We study the effective stress-energy tensor induced by cosmological
inhomogeneity in $f(R)=R+cR^2$ and equivalent scalar-tensor theories, motivated
both by models of early universe inflation and by phenomenological alternative
cosmologies to the standard $\Lambda$-CDM. We use Green and Wald's framework
for averaging over classical fluctuations of short-wavelength $\lambda$. By
ensuring that the leading non-linear terms from the fluctuations of the
Einstein terms and the corrections both contribute in the formal limit as
$\lambda\to0$, we derive a diffeomorphism invariant effective stress-energy
tensor whose trace is non-vanishing and of the right sign to potentially
account for the current acceleration of the universe. However a more
phenomenologically acceptable dark energy model would be required if this
effect were to fully account for the current acceleration.
