The tight-coupling approximation for baryon acoustic oscillations

TL;DR

This paper develops a higher-order tight-coupling approximation for baryon-photon interactions, improving analytical understanding and numerical stability in modeling baryon acoustic oscillations in cosmology.

Contribution

It systematically extends the tight-coupling approximation to higher orders, providing more accurate and stable descriptions of early universe baryon-photon dynamics.

Findings

Higher-order TCA improves numerical stability at early times.

Analytic solutions derived from TCA clarify physical effects.

Vorticity is not generated at lowest order in the extended TCA.

Abstract

The tight-coupling approximation (TCA) used to describe the early dynamics of the baryons-photons system is systematically built to higher orders in the inverse of the interaction rate. This expansion can be either used to grasp the physical effects by deriving simple analytic solutions or to obtain a form of the system which is stable numerically at early times. In linear cosmological perturbations, we estimate numerically its precision, and we discuss the implications for the baryons acoustic oscillations. The TCA can be extended to the second order cosmological perturbations, and in particular we recover that vorticity is not generated at lowest order of this expansion.