Summing Inflationary Logarithms in Nonlinear Sigma Models

Abstract

We consider two nonlinear sigma models on de Sitter background which involve the same derivative interactions as quantum gravity but without the gauge issue. The first model contains only a single field, which can be reduced to a free theory by a local field redefinition; the second contains two fields and cannot be so reduced. Loop corrections in both models produce large temporal and spatial logarithms which cause perturbation theory to break down at late times and large distances. Many of these logarithms derive from the "tail" part of the propagator and can be summed using a variant of Starobinsky's stochastic formalism involving a curvature-dependent effective potential. The remaining logarithms derive from the ultraviolet and can be summed using a variant of the renormalization group based on a special class of curvature-dependent renormalizations. Explicit results are derived at 1-loop and 2-loop orders.

48 pages, 6 figures, uses LaTeX2e, version 2 slightly revised for publication

References in corpus (30)

• Quantum Contributions to Cosmological Correlations II: Can These Corrections Become Large?
• Stochastic Inflationary Scalar Electrodynamics
• On the one loop corrections to inflation and the CMB anisotropies
• Semiclassical relations and IR effects in de Sitter and slow-roll space-times
• Dark energy: a quantum fossil from the inflationary Universe?
• Leading Log Solution for Inflationary Yukawa
• Breakdown of Semiclassical Methods in de Sitter Space
• Quantum Stability of a w < - 1 Phase of Cosmic Acceleration
• On the One Loop Corrections to Inflation II: The Consistency Relation
• On Resumming Inflationary Perturbations beyond One-loop
• Classical approximation to quantum cosmological correlations
• Reply to `Can infrared gravitons screen $\Lambda$?'
• Gravitons Enhance Fermions during Inflation
• Two loop stress-energy tensor for inflationary scalar electrodynamics
• Two Loop Scalar Bilinears for Inflationary SQED
• Can infrared gravitons screen $\Lambda$?
• Quantum Gravity Corrections to the One Loop Scalar Self-Mass during Inflation
• The Zeta-Zeta Correlator Is Time Dependent
• Quantum radiative corrections to slow-roll inflation
• Scalar Field Equations from Quantum Gravity during Inflation
• A Simple Operator Check of the Effective Fermion Mode Function during Inflation
• Excitation of Photons by Inflationary Gravitons
• Cosmology is not a Renormalization Group Flow
• Cosmological Constant Problems and Renormalization Group
• Deducing Cosmological Observables from the S-matrix
• The Weyl tensor correlator in cosmological spacetimes
• One loop graviton corrections to dynamical photons in de Sitter
• Quantum gravity corrections to the conformally coupled scalar self-mass-squared on de Sitter background
• How Inflationary Gravitons Affect Gravitational Radiation
• Gauge Independent Quantum Gravitational Corrections to Maxwell's Equation

Cited by in corpus (16)

• The Open Effective Field Theory of Inflation
• Observations in Quantum Cosmology
• How Inflationary Gravitons Affect the Force of Gravity
• Remembrance of Things Past
• Summing Gravitational Effects from Loops of Inflationary Scalars
• Massless minimal quantum scalar field with an asymmetric self interaction in de Sitter spacetime
• Explaining Large Electromagnetic Logarithms from Loops of Inflationary Gravitons
• Non-perturbative analysis for a massless minimal quantum scalar with $V(\varphi )=\lambda {\varphi }^4/4!+\beta {\varphi }^3/3!$ in the inflationary de Sitter spacetime
• Coincident Massless, Minimally Coupled Scalar Correlators on General Cosmological Backgrounds
• Unfinished Business in A Nonlinear Sigma Model on de Sitter Background
• When tadpoles matter: One-loop corrections for spectator Higgs in inflation
• Resummation of local and non-local scalar self energies via the Schwinger-Dyson equation in de Sitter spacetime
• Big Steve and the State of the Universe
• Large Inflationary Logarithms in a Nontrivial Nonlinear Sigma Model
• Sub-Leading Logarithms for Scalar Potential Models on de Sitter
• Summation of power singularities