Quantum corrections to slow roll inflation and new scaling of superhorizon fluctuations

Abstract

Precise cosmological data from WMAP and forthcoming cosmic microwave background experiments motivate the study of the quantum corrections to the slow roll inflationary parameters. We find the quantum (loop) corrections to the equations of motion of the classical inflaton, to those for the fluctuations and to 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 ϵ V , η V , σ V , ξ 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 Δ = η V − ϵ V = 1 2 ( n s − 1 ) + r / 8 . To leading order in the (EFT) and slow roll expansions we find V eff ( Φ 0 ) = V R ( Φ 0 ) [ 1 + Δ T 2 32 n s − 1 + 3 8 r n s − 1 + 1 4 r + higher orders ] where n s and r = Δ T 2 / Δ R 2 are the CMB observables that depend implicitly on Φ 0 and V R ( Φ 0 ) is the renormalized classical inflaton potential. This effective potential during slow roll inflation is strikingly different from the usual Minkowski space–time result. We also obtain the quantum corrections to the slow roll parameters in leading order. Superhorizon scalar field fluctuations grow for late times η → 0 − as | η | − 1 + Δ − d − where d − is a novel quantum correction to the scaling exponent related to the self-decay of superhorizon inflaton fluctuations φ → φ φ and η is the conformal time. We find to leading order − d − = Δ R 2 σ V ( η V − ϵ V ) + 6 ξ V 2 4 ( η V − ϵ V ) 2 in terms of the CMB observables. These results are generalized to the case of the inflaton interacting with a light scalar field σ and we obtain the decay rate Γ φ → σ σ . These quantum corrections arising from interactions will compete with higher order slow-roll corrections in the Gaussian approximation and must be taken into account for the precision determination of inflationary parameters extracted from CMB observations.