The observational constraint on constant-roll inflation
  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 $\bar\eta\sim 0.01$.
