On the constant-roll inflation

Understand

The primordial power spectra of scalar and tensor perturbations during slow-roll inflation are usually calculated with the method of Bessel function approximation.

• For constant-roll or ultra slow-roll inflation, the method of Bessel function approximation may be invalid.
• We compare the numerical results with the analytical results derived from the Bessel function approximation, and we find that they differ significantly on super-horizon scales if the constant slow-roll parameter $\eta_H$ is not small.
• More accurate method is needed for calculating the primordial power spectrum for constant-roll inflation.