Tensor Mode Backreaction During Slow-roll Inflation

Abstract

We consider the backreaction of the long wavelength tensor modes produced during a slow-roll inflationary regime driven by a single scalar field in a spatially flat Friedmann-Lema\^ıtre-Robertson-Walker background geometry. We investigate the effects on non-local observables such as the effective (averaged) expansion rate and equation of state at second order in cosmological perturbation theory. The coupling between scalar and tensor perturbations induces at second order new tensor backreaction terms beyond the one already present in a de Sitter background. We analyze in detail the effects seen by the class of observers comoving with the inflaton field (taken as a clock) and the class of free-falling observers. In both cases the quantum backreaction is at least $1/\epsilon$ (with $\epsilon$ the slow-roll parameter) larger than the one which can be naively inferred from a de Sitter background. In particular, we compute the effect for a free massive inflaton model and obtain in both cases a quantum correction on the background expansion rate of the order of $H^4/(m^2{M}_{Pl}^2)$. A short discussion on the issue of the breakdown of perturbation theory is given.

6 pages, no figures. Comments, equations and a reference added, typos corrected, some rewording made. Version accepted for publication in PRD

References in corpus (29)

• BICEP2 I: Detection Of B-mode Polarization at Degree Angular Scales
• On average properties of inhomogeneous fluids in general relativity I: dust cosmologies
• Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond
• On the Back Reaction Problem for Gravitational Perturbations
• The Energy-Momentum Tensor for Cosmological Perturbations
• The Quantum Gravitational Back-Reaction On Inflation
• Quantum Gravity Slows Inflation
• Back Reaction And Local Cosmological Expansion Rate
• Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
• Light-cone averaging in cosmology: formalism and applications
• Stochastic growth of quantum fluctuations during slow-roll inflation
• One Loop Graviton Self-Energy In A Locally De Sitter Background
• Back Reaction Of Perturbations In Two Scalar Field Inflationary Models
• No One Loop Back_Reaction In Chaotic Inflation
• Long-wavelength metric backreactions in slow-roll inflation
• A covariant and gauge invariant formulation of the cosmological "backreaction"
• Gauge invariant averages for the cosmological backreaction
• A Scalar Measure Of The Local Expansion Rate
• One Loop Back Reaction On Chaotic Inflation
• Energy-Momentum Tensor of Cosmological Fluctuations during Inflation
• Adiabatic regularization of the graviton stress-energy tensor in de Sitter space-time
• A Phenomenological Model for the Early Universe
• Cosmological Backreaction for a Test Field Observer in a Chaotic Inflationary Model
• Backreaction during inflation: a physical gauge invariant formulation
• The cosmological backreaction: gauge (in)dependence, observers and scalars
• Back-reaction of Cosmological Fluctuations during Power-Law Inflation
• Isotropic Observers and the Inflationary Backreaction Problem
• Pure Gravitational Back-Reaction Observables
• Gauge invariant backreaction in general single field models of inflation

Cited by in corpus (4)

• Back-Reaction of Super-Hubble Cosmological Perturbations Beyond Perturbation Theory
• Graviton Loop Corrections to Vacuum Polarization in de Sitter in a General Covariant Gauge
• Quantum Corrections to the Gravitational Backreaction
• Graviton backreaction on the local cosmological expansion in slow-roll inflation