From stable to unstable anomaly-induced inflation

TL;DR

This paper examines how quantum effects via conformal anomaly influence inflation, showing conditions for stable and unstable phases, and exploring transitions between them with implications for primordial perturbations.

Contribution

It introduces a detailed analysis of stable and unstable anomaly-induced inflation, including mechanisms for transition and the role of large R^2 terms in the inflationary dynamics.

Findings

Unstable inflation requires a large R^2 coefficient (~5×10^8).

Transition from stable to unstable inflation can occur automatically under certain quantum corrections.

The model explains the generation of primordial density perturbations consistent with observations.

Abstract

Quantum effects derived through conformal anomaly lead to an inflationary model that can be either stable or unstable. The unstable version requires a large dimensionless coefficient of about $5\times 10^8$ in front of the $R^2$ term that results in the inflationary regime in the $R+R^2$ ("Starobinsky") model being a generic intermediate attractor. In this case the non-local terms in the effective action are practically irrelevant, and there is a 'graceful exit' to a low curvature matter-like dominated stage driven by high-frequency oscillations of $R$ -- scalarons, which later decay to pairs of all particles and antiparticles, with the amount of primordial scalar (density) perturbations required by observations. The stable version is a genuine generic attractor, so there is no exit from it. We discuss a possible transition from stable to unstable phases of inflation. It is shown that this transition is automatic if the sharp cut-off approximation is assumed for quantum corrections in the period of transition. Furthermore, we describe two different quantum mechanisms that may provide a required large $\,R^2$-term in the transition period.