Anomaly-induced effective action for gravity and inflation

TL;DR

This paper investigates how quantum effects from the trace anomaly influence early Universe inflation, analyzing conformally-flat solutions and their dependence on particle physics models like the Standard Model and supergravity.

Contribution

It provides a detailed derivation of the anomaly-induced effective action for gravity and explores its implications for inflationary cosmology, considering different particle physics scenarios.

Findings

Inflationary solutions are closely linked to the underlying particle physics model.

Quantum trace anomaly effects can naturally lead to inflation without additional fields.

The shape of inflationary solutions depends on the gauge model of elementary particles.

Abstract

In the very early Universe the matter may be described by the free radiation, that is by the set of massless fields with negligible interactions between them. Then the dominating quantum effect is the trace anomaly which comes from the renormalization of the conformal invariant part of the vacuum action. The anomaly-induced effective action can be found with accuracy to an arbitrary conformal functional which vanishes for the special case of the conformally flat metric. This gives the solid basis for the study of the conformally-flat cosmological solutions, first of which was discovered by Mamaev and Mostepanenko and by Starobinski in 1980. Treating the anomaly-induced action as quantum correction to the Einstein-Hilbert term we explore the possibility to have inflationary solutions, investigate their dependence on the initial data and discuss the restrictions in considering the density perturbations. The shape of inflationary solutions strongly depends on the underlying gauge model of the elementary particles physics. Two special cases are considered: Minimal Standard Model and the matter sector of N=8, D=4 supergravity. It turns out that inflation is almost inevitable consequence of the great difference between Planck mass and the mass of the heaviest massive particle.