The Fermion Self-Energy during Inflation

Abstract

We compute the one loop fermion self-energy for massless Dirac + Einstein in the presence of a locally de Sitter background. We employ dimensional regularization and obtain a fully renormalized result by absorbing all divergences with BPHZ counterterms. An interesting technical aspect of this computation is the need for a noninvariant counterterm owing to the breaking of de Sitter invariance by our gauge condition. Our result can be used in the quantum-corrected Dirac equation to search for inflation-enhanced quantum effects from gravitons, analogous to those which have been found for massless, minimally coupled scalars.

arXiv comment63 pages, 3 figures (uses axodraw.sty), LaTeX 2epsilon. Revised version (to appear in Classical and Quantum Gravity) corrects some typoes and contains some new references

References in corpus (33)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• Cosmological Results from High-z Supernovae
• General relativity as an effective field theory: The leading quantum corrections
• Quantum Contributions to Cosmological Correlations
• Equilibrium State of a Massless Self-Interacting Scalar Field in the De Sitter Background
• Leading Quantum Correction to the Newtonian Potential
• 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 Gravity Slows Inflation
• Stochastic Quantum Gravitational Inflation
• Two Loop Scalar Self-Mass during Inflation
• Complementarity of the Maldacena and Randall-Sundrum Pictures
• On the Quantum Corrections to the Newtonian Potential
• One Loop Vaccum Polarization in a Locally de Sitter Background
• Quantum power correction to the Newton law
• One Loop Graviton Self-Energy In A Locally De Sitter Background
• The covariant graviton propagator in de Sitter spacetime
• Production of Massless Fermions during Inflation
• Long Range Forces in Quantum Gravity
• A Leading Logarithm Approximation for Inflationary Quantum Field Theory
• Charged Scalar Self-Mass during Inflation
• Gravitational Waves in Open de Sitter Space
• Long Range Forces from Two Neutrino Exchange Revisited
• Dimensionally Regulated Graviton 1-Point Function in de Sitter
• The physical graviton two-point function in de Sitter spacetime with S^3 spatial sections
• Fermions without Vierbeins in Curved Space-Time
• Quantum long-range interactions in general relativity
• Yukawa Scalar Self-Mass on a Conformally Flat Background
• Cosmological significance of one-loop effective gravity
• Adiabatic regularization of the graviton stress-energy tensor in de Sitter space-time
• Matter Contributions to the Expansion Rate of the Universe
• Accelerated sources in de Sitter spacetime and the insufficiency of retarded fields

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• Quantum Gravity Corrections to the One Loop Scalar Self-Mass during Inflation
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• Perturbative Quantum Gravity Comes of Age
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• Excitation of Photons by Inflationary Gravitons
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• Cosmological UV/IR Divergences and de-Sitter Spacetime
• Graviton Propagator in a General Invariant Gauge on de Sitter
• A Simplified Quantum Gravitational Model of Inflation
• Fermion Propagator in Cosmological Spaces with Constant Deceleration
• Solution of the Dyson--Schwinger equation on de Sitter background in IR limit
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• Weyl-Weyl Correlator in de Donder Gauge on de Sitter
• Issues Concerning Loop Corrections to the Primordial Power Spectra
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• Physical meaning and consequences of the loop IR divergences in global dS
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• Imprint of entanglement entropy in the power spectrum of inflationary fluctuations
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• The Hubble Effective Potential
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• A Caveat on Building Nonlocal Models of Cosmology
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• A graviton propagator for inflation
• 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
• One Loop Field Strengths of Charges and Dipoles on a Locally de Sitter Background
• Representing the Graviton Self-Energy on de Sitter Background
• How Inflationary Gravitons Affect the Force of Gravity
• Generalizing Starobinskii's Formalism to Yukawa Theory & to Scalar QED
• The Graviton Tail almost Completely Wags the Dog
• Fermionic influence (action) on inflationary fluctuations
• The Quantum Corrected Mode Function and Power Spectrum for a Scalar Field during Inflation
• IR Divergence in Inflationary Tensor Perturbations from Fermion Loops
• Regularizing infrared divergences in de Sitter spacetime: Loops, dimensional regularization, and cutoffs
• Single Graviton Loop Contribution to the Self-Mass of a Massless, Conformally Coupled Scalar on de Sitter Background
• Comparative study of loop contributions in AdS and dS
• Primordial Density Perturbations and Reheating from Gravity
• Scheme dependence of quantum gravity on de Sitter background
• The graviton one-loop effective action in cosmological space-times with constant deceleration
• How Inflationary Gravitons Affect Gravitational Radiation
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