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 (6)

• Stochastic Inflationary Scalar Electrodynamics
• On Resumming Inflationary Perturbations beyond One-loop
• Classical approximation to quantum cosmological correlations
• Quantum Gravity Corrections to the One Loop Scalar Self-Mass during Inflation
• Quantum radiative corrections to slow-roll inflation
• Scalar Field Equations from Quantum Gravity during Inflation