Consistency relation for $R^p$ inflation

TL;DR

This paper derives a consistency relation for $R^p$ inflation models near $p=2$, linking key inflationary observables to help distinguish deviations from the $R^2$ inflation scenario in future data.

Contribution

It introduces a new consistency relation for $R^p$ inflation models with $p$ close to 2, aiding observational tests of deviations from $R^2$ inflation.

Findings

Derived a relation between spectral index, tensor-to-scalar ratio, and running.

Provides a tool to constrain deviations from $R^2$ inflation.

Facilitates future observational tests of inflation models.

Abstract

We consider $R^p$ inflation with $p \approx 2$, allowing small deviation from $R^2$ inflation. Using the inflaton potential in the Einstein frame, we construct a consistency relation between the scalar spectral index, the tensor-to-scalar ratio, as well as the running of the scalar spectral index, which will be useful to constrain a deviation from $R^2$ inflation in future observations.