# Secondary isocurvature perturbations from acoustic reheating

## TL;DR

This paper investigates how secondary isocurvature perturbations can be generated during late universe epochs due to violations of standard conditions, especially considering second order effects and heat conduction between baryons and photons.

## Contribution

It introduces second order conserved quantities on superhorizon scales accounting for gradient terms and component non-conservation, with explicit evaluation of heat conduction effects.

## Key findings

- Second order effects can generate isocurvature perturbations from primordial non-Gaussianity.
- Gradient terms are significant even for long wavelength modes due to convolution effects.
- Heat conduction between baryons and photons contributes to secondary isocurvature perturbations.

## Abstract

The superhorizon (iso)curvature perturbations are conserved if the following conditions are satisfied: (i) (each) non adiabatic pressure perturbation is zero, (ii) the gradient terms are ignored, that is, at the leading order of the gradient expansion (iii) (each) total energy momentum tensor is conserved. We consider the case with the violation of the last two requirements and discuss the generation of secondary isocurvature perturbations during the late time universe. Second order gradient terms are not necessarily ignored even if we are interested in the long wavelength modes because of the convolutions which may pick products of short wavelength perturbations up. We then introduce second order conserved quantities on superhorizon scales under the conditions (i) and (iii) even in the presence of the gradient terms by employing the full second order cosmological perturbation theory. We also discuss the violation of the condition (iii), that is, the energy momentum tensor is conserved for the total system but not for each component fluid. As an example, we explicitly evaluate second order heat conduction between baryons and photons due to the weak Compton scattering, which dominates the period just before recombination. We show that such secondary effects can be recast into the isocurvature perturbations on superhorizon scales if the local type primordial non Gaussianity exists a priori.