An Analytic Treatment of Underdamped Axionic Blue Isocurvature Perturbations

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. Contents 1. Introduction 2. A brief review of blue axionic isocurvature perturbations 3. Decoupling 4. Behavior of φ ± near the first crossing of φ ± 4.1. Perturbative solution 4.2. Beyond perturbation theory 4.3. Resonant scenarios 5. Numerically Motivated model 5.1. Piecewise solution (scattering matrix approach) 5.2. Independent analytic functions in each piecewise-region

Gravitational waves from dark matter isocurvature

“…[21][22][23][24][25][26] for recent reviews). Large isocurvature fluctuations may be a consequence of phase transitions [27], light spectator fields during inflation [28,29], or clustering of Q-balls [30], though forming sufficiently large fluctuations for this mechanism to function may be challenging.…”

Probing isocurvature perturbations with 21-cm global signal in the light of HERA result

“…(2.6), which arises in CDM axion models. Although such models generally predict n iso ∼ 1, blue-tilted spectra can also be predicted in some scenarios [2][3][4][5]. Therefore we take n iso as a free parameter as well as r CDM to characterize the statistical property of the isocurvature perturbations.…”

“…However, observations of CMB can only probe fluctuations on large scales. Indeed some scenarios of the early Universe predict isocurvature fluctuations with a blue-tilted spectrum which includes axion [2][3][4][5], primordial black holes (PBHs) [6][7][8][9], and so on. In this kind of models, isocurvature fluctuations can give sizable contribution only on small scales whereas they scarcely affect large scale fluctuations which are severely constrained by CMB, and hence it is imperative to test those scenarios by observations of small scales fluctuations.…”

Gravitational waves from dark matter isocurvature

“…[21][22][23][24][25][26] for recent reviews). Large isocurvature fluctuations may be a consequence of phase transitions [27], light spectator fields during inflation [28,29], or clustering of Q-balls [30], though forming sufficiently large fluctuations for this mechanism to function may be challenging.…”