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

Abstract

We 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 quantum fluctuations from light scalars and light Dirac fermions generically coupled to the inflaton. During slow roll inflation there is a clean and unambiguous separation between superhorizon 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 quantum corrections to the amplitude of curvature and tensor perturbations are obtained to leading order in slow-roll and in the (H/M_PL)^2 expansion. This study provides a complete assessment of the backreaction problem up to one loop including bosonic and fermionic degrees of freedom. 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:n_s, r and dn_s/dln 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.

arXiv comment18 pages, no figures

References in corpus (29)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• Particle Physics Models of Inflation and the Cosmological Density Perturbation
• Non-Gaussianity from Inflation: Theory and Observations
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Inflation
• Wilkinson Microwave Anisotropy Probe (WMAP) First Year Observations: TE Polarization
• Reconstructing the Inflaton Potential --- an Overview
• The Cold Dark Matter Density Perturbation
• Formalising the Slow-Roll Approximation in Inflation
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Tests of Gaussianity
• A more accurate analytic calculation of the spectrum of cosmological perturbations produced during inflation
• A note on inflation and transplanckian physics
• The Robustness of Inflation to Changes in Super-Planck-Scale Physics
• The Energy-Momentum Tensor for Cosmological Perturbations
• Analytic and Numerical Study of Preheating Dynamics
• Reheating and Thermalization, Linear Vs. Non-Linear Relaxation
• Non-Equilibrium Evolution of Scalar Fields in FRW Cosmologies I
• Scalar Field Dynamics in Friedman Robertson Walker Spacetimes
• Nonequilibrium inflaton dynamics and reheating: Back reaction of parametric particle creation and curved spacetime effects
• Effective Field Theories and Inflation
• Non-Perturbative Quantum Dynamics of a New Inflation Model
• Short distance and initial state effects in inflation: stress tensor and decoherence
• O(N) Quantum fields in curved spacetime
• Particle decay during inflation: self-decay of inflaton quantum fluctuations during slow roll
• Particle decay in inflationary cosmology
• Initial state of matter fields and trans-Planckian physics: Can CMB observations disentangle the two?
• Theoretical tools for CMB physics
• Adiabatic regularization of the graviton stress-energy tensor in de Sitter space-time
• Renormalization of the nonequilibrium dynamics of fermions in a flat FRW universe
• The Classical and Quantum Inflaton: the Precise Inflationary Potential and Quantum Inflaton Decay after WMAP

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• Large non-Gaussianities in the Effective Field Theory Approach to Single-Field Inflation: the Bispectrum
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• One-loop Corrections to Scalar and Tensor Perturbations during Inflation in Stochastic Gravity
• An effective field theory during inflation II: stochastic dynamics and power spectrum suppression
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