Backreaction and Stochastic Effects in Single Field Inflation
  The formalism of stochastic inflation is a powerful tool for analyzing the
backreaction of cosmological perturbations, and making precise predictions for
inflationary observables. We demonstrate this with the simple $m^2\phi^2$ model
of inflation, wherein we obtain an effective field theory for IR modes of the
inflaton, which remains coupled to UV modes through a classical noise. We
compute slow-roll corrections to the evolution of UV modes (i.e. quantum
fluctuations), and track this effect from the UV theory to the IR theory, where
it manifests as a correction to the classical noise. We compute the stochastic
correction to the spectral index of primordial perturbations, finding a small
effect, and discuss models in which this effect can become large. We extend our
analysis to tensor modes, and demonstrate that the stochastic approach allows
us to recover the standard tensor tilt $n_T$, plus corrections.
