Dark Matter Isocurvature from Curvature

TL;DR

This paper develops a simple method to calculate dark matter isocurvature fluctuations generated from curvature perturbations, analyzing their amplitude across different epochs and models, and finds freeze-out models can produce larger fluctuations than freeze-in models.

Contribution

It introduces a separate-universe approach to compute dark matter isocurvature from curvature fluctuations, applicable to various thermal history scenarios and models.

Findings

Freeze-out models can produce larger isocurvature fluctuations than freeze-in models.

The amplitude of isocurvature fluctuations depends on the epoch: freezing, kinetic decoupling, or matter-radiation equality.

Fluctuations are generally small but within observational bounds from CMB measurements.

Abstract

Isocurvature fluctuations, where the relative number density of particle species spatially varies, can be generated from initially adiabatic, or curvature, fluctuations if the various species fall out of or were never in thermal equilibrium. The freezing of the thermal relic dark matter abundance is one such case, but for modes that are still outside the horizon the amplitude is highly suppressed and originates from the small change in the local expansion rate due to the local space curvature produced by the curvature fluctuation. We establish a simple separate-universe method for calculating this generation that applies to both freeze-in and freeze-out models, identify three critical epochs for this process, and give general scaling behaviors for the amplitude in each case: the freezing epoch, the kinetic decoupling epoch and matter-radiation equality. Freeze-out models are typically dominated by spatially modulated annihilation from the latter epochs and can generate much larger isocurvature fluctuations compared with typical freeze-in models, albeit still very small and observationally allowed by cosmic microwave background measurements. We illustrate these results with concrete models where the dark matter interactions are vector or scalar mediated.