Quantum corrections during inflation and conservation of adiabatic perturbations

TL;DR

This paper investigates whether quantum corrections during inflation can break the conservation of superhorizon adiabatic perturbations, focusing on one-loop effects from massless fields and their implications for the power spectrum and symmetries.

Contribution

It analyzes quantum corrections in single field inflation, emphasizing renormalization and the potential impact of trace anomalies on perturbation conservation.

Findings

Possible secular dependence of the power spectrum due to trace anomaly

Renormalization yields zero tadpole value

Quantum corrections do not violate dilatation invariance

Abstract

The possibility that quantum corrections break the conservation of superhorizon adiabatic perturbations in single field inflation is examined. I consider the lowest order corrections from massless matter fields in the Hamiltonian formalism. Particular emphasis is therefore laid on the renormalization. The counterterms are the same as in the Lagrangian formalism. The renormalized value of the tadpole is zero. I find a possible secular dependence of the power spectrum at one loop due to the trace anomaly, but this result depends on the approximation of the modes and is inconclusive. The symmetry (not) violated by the quantum corrections is the invariance by dilatation. Perspectives on the backreaction problem are briefly discussed.