An Analytic Treatment of Underdamped Axionic Blue Isocurvature
  Perturbations
  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.
