Cosmological Backreaction for a Test Field Observer in a Chaotic
  Inflationary Model
  In an inhomogeneous universe, an observer associated with a particular matter
field does not necessarily measure the same cosmological evolution as an
observer in a homogeneous and isotropic universe. Here we consider, in the
context of a chaotic inflationary background model, a class of observers
associated with a "clock field" for which we use a light test field. We compute
the effective expansion rate and fluid equation of state in a gauge invariant
way, taking into account the quantum fluctuations of the long wavelength modes,
and working up to second order in perturbation theory and in the slow-roll
approximation. We find that the effective expansion rate is smaller than what
would be measured in the absence of fluctuations. Within the stochastic
approach we study the bounds for which the approximations we make are
consistent.
