On the scaling rules for the anomaly-induced effective action of metric and electromagnetic field

TL;DR

This paper investigates how quantum anomalies influence the effective gravitational action, particularly in the presence of electromagnetic fields, revealing that the anomaly-induced effects scale similarly to the cosmological constant.

Contribution

It derives the scaling laws for the anomaly-induced effective action in the presence of electromagnetic fields, extending understanding of quantum corrections in cosmological models.

Findings

Anomaly-induced effective action scales like the cosmological constant.

Electromagnetic fields disrupt exponential inflation driven by quantum corrections.

Derived the equation of state and scaling laws for Einstein equations with anomaly effects.

Abstract

The anomaly-induced effective action is a useful tool for deriving the contributions coming from quantum effects of massless conformal fields. It is well-known that such corrections in the higher derivative vacuum sector of the gravitational action provide the same exponential inflation (Starobinsky model) as the cosmological constant term. At the same time, the presence of a classical electromagnetic field breaks down the exponential solution. In this paper we explore the role of the anomaly-induced term in the radiation sector and, furthermore, derive the ``equation of state'' and the scaling laws for all terms in the Einstein equations. As one could expect, the scaling law for the vacuum anomaly-induced effective action is the same as for the cosmological constant.