The observational constraint on constant-roll inflation

TL;DR

This paper analyzes constant-roll inflation models with specific parameters, deriving analytical expressions for power spectra and spectral tilts, and compares their observational viability, finding that only the model with constant ta is consistent with current data.

Contribution

The paper provides analytical expressions for scalar and tensor spectra in constant-roll inflation and assesses their observational constraints, highlighting the viability of the constant ta model.

Findings

Constant ta model fits observations at 1onfidence level.

Constant psilon_2 model is ruled out at 3onfidence level.

The spectral index and tensor-to-scalar ratio differ from slow-roll predictions even for small ta.

Abstract

We discuss the constant-roll inflation with constant $\epsilon_2$ and constant $\bar\eta$. By using the method of Bessel function approximation, the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts, and the tensor to scalar ratio are derived up to the first order of $\epsilon_1$. The model with constant $\epsilon_2$ is ruled out by the observations at the $3\sigma$ confidence level, and the model with constant $\bar\eta$ is consistent with the observations at the $1\sigma$ confidence level. The potential for the model with constant $\bar\eta$ is also obtained from the Hamilton-Jacobi equation. Although the observations constrain the constant-roll inflation to be slow-roll inflation, the $n_s-r$ results from the constant-roll inflation are not the same as those from the slow-roll inflation even when $\bar\eta\sim 0.01$.