The observational constraint on constant-roll inflation

Understand

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.