Effective field theory during inflation. II. Stochastic dynamics and power spectrum suppression

We obtain the nonequilibrium effective action of an inflatonlike scalar field-the system-by tracing over sub-Hubble degrees of freedom of "environmental" light scalar fields. The effective action is stochastic leading to effective Langevin equations of motion for the fluctuations of the inflatonlike field, with self-energy corrections and stochastic noise correlators that obey a de Sitter space-time analog of a fluctuation dissipation relation. We solve the Langevin equation implementing a dynamical renormalization group resummation of the leading secular terms and obtain the corrections to the power spectrum of super-Hubble fluctuations of the inflaton field, P(k;eta) = P-0(k)e(-gamma(k;eta)) where P-0(k) is the nearly scale invariant power spectrum in absence of coupling. gamma(k;eta) > 0 describes the suppression of the power spectrum; it features Sudakov-type double logarithms and entails violations of scale invariance. We also obtain the effective action for the case of a heavy scalar field of mass M >> H; this case yields a local "Fermi" limit with a very weak self-interaction of the inflatonlike field and dissipative terms that are suppressed by powers of H/M. We conjecture on the possibility that the large scale anomalies in the cosmic microwave background may originate in dissipative processes from inflaton coupling to sub-Hubble degrees of freedom.