The Quantum-Corrected Fermion Mode Function during Inflation

Abstract

My project computed the one loop fermion self-energy for massless Dirac + Einstein in the presence of a locally de Sitter background. I employed dimensional regularization and obtain a fully renormalized result by absorbing all divergences with Bogliubov, Parasiuk, Hepp and Zimmermann (BPHZ) counterterms. An interesting technical aspect of my computation was the need for a noninvariant counterterm, owing to the breaking of de Sitter invariance by our gauge condition. I also solved the effective Dirac equation for massless fermions during inflation in the simplest gauge, including all one loop corrections from quantum gravity. At late times the result for a spatial plane wave behaves as if the classical solution were subjected to a time-dependent field strength renormalization of Z_2(t) = 1 - 17(4 pi) *G H^2 *ln(a) + O(G^2). I showed that this also follows from making the Hartree approximation, although the numerical coefficients differ.

Ph.D. thesis

References in corpus (4)

• Quantum Gravity In De Sitter Space
• Quantum Stability of a w < - 1 Phase of Cosmic Acceleration
• Cosmological long wavelength perturbations
• Quantum Cosmological Correlations in an Inflating Universe: Can fermion and gauge fields loops give a scale free spectrum?

Cited by in corpus (15)

• Infrared Propagator Corrections for Constant Deceleration
• A Completely Regular Quantum Stress Tensor with $w<-1$
• Excitation of Photons by Inflationary Gravitons
• A Simplified Quantum Gravitational Model of Inflation
• Graviton Loop Corrections to Vacuum Polarization in de Sitter in a General Covariant Gauge
• The Coincidence Limit of the Graviton Propagator in de Donder Gauge on de Sitter Background
• Covariant Vacuum Polarizations on de Sitter Background
• One-loop quantum electrodynamic correction to the gravitational potentials on de Sitter spacetime
• Hartree Approximation to the One Loop Quantum Gravitational Correction to the Graviton Mode Function on de Sitter
• Deducing Cosmological Observables from the S-matrix
• Representing the Vacuum Polarization on de Sitter
• One Loop Field Strengths of Charges and Dipoles on a Locally de Sitter Background
• Representing the Graviton Self-Energy on de Sitter Background
• Alternate Definitions of Loop Corrections to the Primordial Power Spectra
• Strange Work in Strange Places: Quantum Field Theory in Curved Space