An Analytic Treatment of Underdamped Axionic Blue Isocurvature Perturbations

TL;DR

This paper analytically explores the underdamped regime of axionic isocurvature perturbations during inflation, revealing resonant spectral behaviors and complex spectral shapes not previously characterized.

Contribution

It provides the first analytical treatment of the underdamped axionic isocurvature spectrum, including the discovery of resonant spectral features in this regime.

Findings

Identification of resonant spectral behavior in underdamped regime

Analytical computation of the spectrum in a large parametric region

Discovery of complex isocurvature spectral shapes

Abstract

Previous computations of strongly blue tilted axionic isocurvature spectra were computed in the parametric region in which the lightest time-dependent mass is smaller than the Hubble expansion rate during inflation, leading to an overdamped time evolution. Here we present the strongly blue tilted axionic isocurvature spectrum in an underdamped time evolution parametric regime. Somewhat surprisingly, there exist parametric regions with a strong resonant spectral behavior that leads to a rich isocurvature spectral shape. We focus on computing this resonant spectrum analytically in a large parametric region amenable to such computations. Because the spectrum is sensitive to nonperturbative classical field dynamics, a wide variety of analytic techniques are used including a time-space effective potential obtained by integrating out high frequency fluctuations.