Cosmological Perturbations at Second Order and Recombination Perturbed

TL;DR

This paper derives second-order cosmological perturbation equations, focusing on electron density perturbations during recombination, revealing significant enhancements in  perturbations that impact CMB bispectrum calculations.

Contribution

It provides a comprehensive derivation of second-order perturbation equations including  effects and analyzes their impact on recombination and CMB anisotropies.

Findings

 perturbations are enhanced by a factor of ~5 during recombination.

Perturbed Ly escape probability is mainly governed by local baryon velocity divergence.

A perturbed 3-level atom model suffices for small-scale modes (<1 Mpc^{-1}).

Abstract

We derive the full set of second-order equations governing the evolution of cosmological perturbations, including the effects of the first-order electron number density perturbations, \delta_e. We provide a detailed analysis of the perturbations to the recombination history of the universe and show that a perturbed version of the Peebles effective 3-level atom is sufficient for obtaining the evolution of \delta_e for comoving wavenumbers smaller than 1Mpc^{-1}. We calculate rigorously the perturbations to the Ly\alpha escape probability and show that to a good approximation it is governed by the local baryon velocity divergence. For modes shorter than the photon diffusion scale, we find that \delta_e is enhanced during recombination by a factor of roughly 5 relative to other first-order quantities sourcing the CMB anisotropies at second order. Using these results, in a companion paper we calculate the CMB bispectrum generated during recombination.