Constant-Roll Inflation: Analytical Formulae for Power Spectrum and Implications for Induced Gravitational Waves

Abstract

Constant-roll inflation provides a simple and analytically tractable framework for describing transient departures from slow roll, including non-attractor phases that can enhance the primordial curvature perturbation on small scales. In this work, we investigate the curvature power spectrum generated in a slow-roll--constant-roll--slow-roll scenario, focusing on the positions and amplitudes of the two characteristic peaks associated with the two transitions. We show that, in the parameter range where both peaks are well separated and sufficiently pronounced, the underlying constant-roll parameters can be reconstructed from the peak positions and amplitudes without performing a brute-force parameter scan. In addition, we construct a smoothed analytic approximation to the power spectrum, designed for efficient estimates of scalar-induced gravitational waves and related phenomenological applications.