Quantum corrections to the inflaton potential and the power spectra from superhorizon modes and trace anomalies

International audienceWe obtain the effective inflaton potential during slow-roll inflation by including the one-loop quantum corrections to the energy momentum tensor from scalar curvature and tensor perturbations as well as from light scalars and Dirac fermions coupled to the inflaton. During slow-roll inflation there is an unambiguous separation between super- and subhorizon contributions to the energy momentum tensor. The superhorizon part is determined by the curvature perturbations and scalar field fluctuations: both feature infrared enhancements as the inverse of a combination of slow-roll parameters which measure the departure from scale invariance in each case. Fermions and gravitons do not exhibit infrared divergences. The subhorizon part is completely specified by the trace anomaly of the fields with different spins and is solely determined by the space-time geometry. The one-loop corrections to the amplitude of curvature and tensor perturbations are obtained to leading order in slow roll and in the (H/MPl)2 expansion. A complete assessment of the backreaction problem up to one loop including bosons and fermions is provided. The result validates the effective field theory description of inflation and confirms the robustness of the inflationary paradigm to quantum fluctuations. Quantum corrections to the power spectra are expressed in terms of the CMB observables: ns, r and dns/dlnf k. Trace anomalies (especially the graviton part) dominate these quantum corrections in a definite direction: they enhance the scalar curvature fluctuations and reduce the tensor fluctuations