  We calculate the back-reaction of long wavelength cosmological perturbations on a general relativistic measure of the local expansion rate of the Universe. Specifically, we consider a cosmological model in which matter is described by two scalar matter fields, one being the inflaton and the other one representing a matter field which is used as a clock. We analyze back-reaction in a phase of inflaton-driven slow-roll inflation, and find that the leading infrared back-reaction terms contributing to the evolution of the expansion rate do not vanish when measured at a fixed value of the clock field. We also analyze the back-reaction of entropy modes in a specific cosmological model with negative square mass for the entropy field and find that back-reaction can become significant. Our work provides evidence that, in general, the back-reaction of infrared fluctuations could be locally observable. 
Back Reaction Of Perturbations In Two Scalar Field Inflationary Models