Scalaron from $R^2$-gravity as a Heavy Field

TL;DR

This paper investigates a two-field inflation model involving a scalaron from $R^2$ gravity and a non-minimally coupled scalar, revealing how oscillations during transition stages affect the curvature perturbation spectrum and potential observational signatures.

Contribution

It introduces a novel inflationary scenario with a scalaron and a non-minimally coupled scalar, analyzing the transition dynamics and resulting power spectrum features.

Findings

Oscillations during inflation transition cause features in the power spectrum.

Perturbative calculation of spectral features using the $ abla$ formalism.

Potential implications for CMB anomalies and primordial black holes.

Abstract

We study a model of inflation in which a scalar field $\chi$ is non-minimally coupled to Starobinsky's $R^2$ gravity. After transforming it to the Einstein frame, a new scalar field, the scalaron $\phi$, will appear and couple to $\chi$ with a nontrivial field metric, while $\chi$ acquires a positive mass via the non-minimal coupling. Initially inflation occurs along the $\phi$ direction with $\chi$ trapped near its origin by this induced mass. After $\phi$ crosses a critical value, it starts rolling down rapidly and proceeds todamped oscillations around an effective local minimum determined by the value of $\chi$, while inflation still continues, driven by the $\chi$ field at this second stage where the effect of the non-minimal coupling becomes negligible. The presence of the damped oscillations during the transition from the first to second stage of inflation causes enhancement and oscillation features in the power spectrum of the curvature perturbation. Assuming that the oscillations may be treated perturbatively, we calculate these features by using the $\delta N$ formalism, and discuss its observational implications to large scale CMB anomalies or primordial black hole formation, depending on the scale of the features.