Backreaction during inflation: a physical gauge invariant formulation
  Within a genuinely gauge invariant approach recently developed for the computation of the cosmological backreaction, we study, in a cosmological inflationary context and with respect to various observers, the impact of scalar fluctuations on the space-time dynamics in the long wavelength limit. We stress that such a quantum backreaction effect is evaluated in a truly gauge independent way using a set of effective equations which describe the dynamics of the averaged geometry. In particular we show under what conditions the free falling (geodetic) observers do not experience any scalar-induced backreaction in the effective Hubble rate and fluid equation of state. 
F. Finelli, G. Marozzi, G. P. Vacca, G. Venturi
gr-qc astro-ph.CO hep-th