Precision Predictions for the Primordial Power Spectra from f(R) Models of Inflation

TL;DR

This paper introduces a new analytical technique to accurately predict the primordial power spectra in f(R) inflation models, highlighting differences between Jordan and Einstein frames and implications for observational data.

Contribution

It develops a novel method for calculating power spectra in f(R) inflation, providing precise analytic approximations and exploring frame-dependent differences.

Findings

Spectra are numerically identical in Jordan and Einstein frames for the same wave number.

Power spectra depend differently on the number of e-foldings in the two frames.

Future reheating data can distinguish f(R) inflation from scalar-driven inflation.

Abstract

We study the power spectra of f(R) inflation using a new technique in which the norm-squared of the mode functions is evolved. Our technique results in excellent analytic approximations for how the spectra depend upon the function $f(R)$. Although the spectra are numerically the same in the Jordan and Einstein frames for the same wave number $k$, they depend upon the geometries of these frames in quite different ways. For example, the power spectra in the two frames are different functions of the number of e-foldings until end of inflation. We discuss how future data on reheating can be used to distinguish f(R) inflation from scalar-driven inflation.