  Precise cosmological data from WMAP and forthcoming CMB experiments motivate
the study of the quantum corrections to the slowroll inflationary parameters.We
find the quantum (loop) corrections to the equations of motion of the classical
inflaton, its quantum fluctuations and the Friedmann equation in general single
field slow roll inflation.We implement a renormalized effective field theory
EFT approach based on an expansion in (H/M_{Pl})^2 and slow roll parameters
epsilon_V,eta_V,sigma_V, xi_V.We find that the leading order quantum
corrections to the inflaton effective potential and its equation of motion are
determined by the power spectrum of scalar fluctuations. Its near scale
invariance introduces a strong infrared behavior naturally regularized by the
slow roll parameter Delta = eta_V-epsilon_V=(n_s-1)/2+r/8.To leading order in
the EFT and slow roll expansions we find
V_{eff}(Phi_0)=V_R(Phi_0)[1+(Delta^2_T/32)(n_s-1+3r/8) /(n_s-1+r/4)+higher
orders]where n_s and r=Delta^2_T/Delta^2_R are the CMB observables that depend
implicitly on Phi_0, and V_R(Phi_0) is the renormalized classical inflaton
potential.This effective potential during slow roll inflation is strikingly
different from the Minkowski space-time result.Superhorizon scalar field
fluctuations grow for late times eta -> 0^- as |\eta|^{-1+Delta-d_} where d_ is
a novel quantum correction to the scaling exponent related to the self decay of
superhorizon inflaton fluctuations eta is the conformal time. We generalize
this to the case of the inflaton interacting with a light scalar field. These
quantum corrections arising from interactions will compete with higher order
slow-roll corrections and must be taken into account for the precision
determination of inflationary parameters.
