  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.
