Renormalization of the inflationary perturbations revisited

Abstract

In this work we clarify aspects of renormalization on curved backgrounds focussing on the potential ramifications on the amplitude of inflationary perturbations. We provide an alternate view of the often used adiabatic prescription by deriving a correspondence between the adiabatic subtraction terms and traditional renormalization. Specifically, we show how adiabatic subtraction can be expressed as a set of counter terms that are introduced by redefining the bare parameters of the action. Our representation of adiabatic subtraction then allows us to easily find other renormalization prescriptions differing only in the finite parts of the counter terms. As our main result, we present for quadratic inflation how one may consistently express the renormalization of the spectrum of perturbations from inflation as a redefinition of the bare cosmological constant and Planck mass such that the observable predictions coincide with the unrenormalized result.

v1: 17 pages. v2: 17 pages, minor improvements, updated references. v3: 19 pages, added discussion, version accepted for publication in JCAP

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• A manifestly covariant theory of multifield stochastic inflation in phase space: solving the discretisation ambiguity in stochastic inflation
• Realisation of the ultra-slow roll phase in Galileon inflation and PBH overproduction
• Large fluctuations and Primordial Black Holes
• Adiabatic regularization of power spectrum and stress tensor of relic gravitational wave without low-frequency distortion
• Point-splitting regularization of the stress tensor of a coupling scalar field in de Sitter space
• The effect of quantum decoherence on inflationary gravitational waves
• On the adiabatic subtraction of cosmological perturbations
• Regularized stress tensor of vector fields in de Sitter space
• Physical scale adiabatic regularization in cosmological spacetimes
• Induced energy-momentum tensor in de Sitter scalar QED and its implication for induced current