A Simple Operator Check of the Effective Fermion Mode Function during Inflation

Abstract

We present a relatively simple operator formalism which reproduces the leading infrared logarithm of the one loop quantum gravitational correction to the fermion mode function on a locally de Sitter background. This rule may serve as the basis for an eventual stochastic formulation of quantum gravity during inflation. Such a formalism would not only effect a vast simplification in obtaining the leading powers of $\ln (a)$ at fixed loop orders, it would also permit us to sum the series of leading logarithms. A potentially important point is that our rule does not seem to be consistent with any simple infrared truncation of the fields. Our analysis also highlights the importance of spin as a gravitational interaction that persists even when kinetic energy has redshifted to zero.

39 pages, no figuire.(1) New version has clarified the ultimate motivation by adding sentences to the abstract and to the penultimate paragraph of the introduction. (2) By combining a number of references and equations we have managed to reduce the length by 2 pages

References in corpus (45)

• Quantum Contributions to Cosmological Correlations
• Equilibrium State of a Massless Self-Interacting Scalar Field in the De Sitter Background
• Quantum effects can render w<-1 on cosmological scales
• Super-Acceleration from Massless, Minimally Coupled ${\varphi }^4$
• The Quantum Gravitational Back-Reaction On Inflation
• Quantum Contributions to Cosmological Correlations II: Can These Corrections Become Large?
• Quantum Gravity Slows Inflation
• Stochastic Quantum Gravitational Inflation
• Stochastic Inflationary Scalar Electrodynamics
• On the one loop corrections to inflation and the CMB anisotropies
• Two Loop Scalar Self-Mass during Inflation
• Leading Log Solution for Inflationary Yukawa
• Photon mass from inflation
• Large non-Gaussianity in multiple-field inflation
• One Loop Vaccum Polarization in a Locally de Sitter Background
• Stationary Universe
• Quantum Stability of a w < - 1 Phase of Cosmic Acceleration
• On the divergences of inflationary superhorizon perturbations
• The Fermion Self-Energy during Inflation
• Quantum corrections to slow roll inflation and new scaling of superhorizon fluctuations
• On Resumming Inflationary Perturbations beyond One-loop
• Scalar Field Dynamics in Friedman Robertson Walker Spacetimes
• Non-linear perturbations in multiple-field inflation
• One Loop Graviton Self-Energy In A Locally De Sitter Background
• Classical approximation to quantum cosmological correlations
• Gravitons Enhance Fermions during Inflation
• Production of Massless Fermions during Inflation
• Quantum corrections to the inflaton potential and the power spectra from superhorizon modes and trace anomalies
• Effective noise in stochastic description of inflation
• A Leading Logarithm Approximation for Inflationary Quantum Field Theory
• Two Loop Scalar Bilinears for Inflationary SQED
• Dynamics of super-horizon photons during inflation with vacuum polarization
• Fermion Mass Generation in de Sitter Space
• Quantum Gravity Corrections to the One Loop Scalar Self-Mass during Inflation
• Stress Tensor Correlators in the Schwinger-Keldysh Formalism
• Charged Scalar Self-Mass during Inflation
• Quantum radiative corrections to slow-roll inflation
• Dimensionally Regulated Graviton 1-Point Function in de Sitter
• Scalar Field Equations from Quantum Gravity during Inflation
• One Loop Corrected Mode Functions for SQED during Inflation
• Photon mass generation during inflation: de Sitter invariant case
• Simple route to non-Gaussianity in inflation
• Quantum Cosmological Correlations in an Inflating Universe: Can fermion and gauge fields loops give a scale free spectrum?
• Yukawa Scalar Self-Mass on a Conformally Flat Background
• On the Reliability of the Langevin Pertubative Solution in Stochastic Inflation

Cited by in corpus (53)

• Observational Viability and Stability of Nonlocal Cosmology
• Infrared Propagator Corrections for Constant Deceleration
• Perturbative Quantum Gravity Comes of Age
• The Zeta-Zeta Correlator Is Time Dependent
• A Completely Regular Quantum Stress Tensor with $w<-1$
• The Graviton Propagator in de Donder Gauge on de Sitter Background
• The Perils of Analytic Continuation
• Excitation of Photons by Inflationary Gravitons
• Vacuum Fluctuations of a Scalar Field during Inflation: Quantum versus Stochastic Analysis
• Graviton Propagator in a General Invariant Gauge on de Sitter
• A Simplified Quantum Gravitational Model of Inflation
• A Phenomenological Model for the Early Universe
• Issues Concerning Loop Corrections to the Primordial Power Spectra
• Weyl-Weyl Correlator in de Donder Gauge on de Sitter
• Linearized Weyl-Weyl Correlator in a de Sitter Breaking Gauge
• Quantum Gravitational Effects on Massive Fermions during Inflation I
• Quantum Scalar Corrections to the Gravitational Potentials on de Sitter Background
• Graviton Corrections to Maxwell's Equations
• Summing Inflationary Logarithms in Nonlinear Sigma Models
• The Coincidence Limit of the Graviton Propagator in de Donder Gauge on de Sitter Background
• The Hubble Effective Potential
• Soft Gravitons Screen Couplings in de Sitter Space
• Nonlocal Metric Realizations of MOND
• Inflationary Scalars Don't Affect Gravitons at One Loop
• Covariant Vacuum Polarizations on de Sitter Background
• A Caveat on Building Nonlocal Models of Cosmology
• Hartree Approximation to the One Loop Quantum Gravitational Correction to the Graviton Mode Function on de Sitter
• Soft Graviton effects on Gauge theories in de Sitter Space
• Deducing Cosmological Observables from the S-matrix
• Representing the Vacuum Polarization on de Sitter
• Time Dependent Couplings as Observables in de Sitter Space
• Quantum gravity corrections to the conformally coupled scalar self-mass-squared on de Sitter II: kinetic-conformal cross terms
• Quantum gravity corrections to the conformally coupled scalar self-mass-squared on de Sitter background
• Representing the Graviton Self-Energy on de Sitter Background
• The Graviton Tail almost Completely Wags the Dog
• Quantum Effects of Mass on Scalar Field Correlations and Fluctuations during Inflation
• Single Graviton Loop Contribution to the Self-Mass of a Massless, Conformally Coupled Scalar on de Sitter Background
• Scheme dependence of quantum gravity on de Sitter background
• Primordial Density Perturbations and Reheating from Gravity
• How Inflationary Gravitons Affect Gravitational Radiation
• Summing Gravitational Effects from Loops of Inflationary Scalars
• Soft gravitational effects in Kadanoff-Baym approach
• Graviton Self-Energy from Gravitons in Cosmology
• Stochastic Samples versus Vacuum Expectation Values in Cosmology
• Unfinished Business in A Nonlinear Sigma Model on de Sitter Background
• Quantum corrections during inflation and conservation of adiabatic perturbations
• Coincident Massless, Minimally Coupled Scalar Correlators on General Cosmological Backgrounds
• One loop corrected conformally coupled scalar mode equations during inflation
• Possible Enhancement of High Frequency Gravitational Waves
• Testing an Ansatz for the Leading Secular Loop Corrections from Quantum Gravity during Inflation
• Big Steve and the State of the Universe
• Causality Implies Inflationary Back-Reaction
• Effective Lagrangian in de Sitter Spacetime