Inflationary behavior of $R^2$ gravity in a conformal framework

TL;DR

This paper investigates the inflationary behavior of $R^2$ gravity within a conformal framework, demonstrating its robustness against additional scalar fields, but noting that precise data agreement depends on parameter choices.

Contribution

It shows that conformal gravitational theories with $R^2$ terms maintain inflationary behavior despite extra scalar fields, extending the Starobinsky model's applicability.

Findings

$R^2$ inflation remains stable with additional scalar fields.

Exact data fit depends on parameter tuning.

Conformal anomaly origin of $R^2$ terms is significant.

Abstract

Models of inflation are tightly constrained by the PLANCK satellite data. Among them, Starobinsky's model with an exponential type potential seems to be challenged by the recent BICEP2 results. The model is based on the existence of $\,~ R^2$ terms in the Einstein-Hilbert action, which have their origin in the conformal-anomaly. Conformal (or Weyl) gravitational theories are relevant when matter fields become effectively massless; i.e. their masses are negligible in comparison with the spacetime curvature. These theories may include other, additional scalar fields. We show that their presence under general conditions does not destabilize the inflationary behaviour encountered in the Starobinsky model, although the issue of the exact quantitative agreement with existing data, like the tensor to scalar ratio, rests on the choice of parameters.