A Simple Analytic Treatment of Linear Growth of Structure with Baryon Acoustic Oscillations

TL;DR

This paper introduces an analytical framework for modeling the linear growth of cosmic structure across all scales, including those relevant for baryon acoustic oscillations, improving upon previous numerical and phenomenological methods.

Contribution

It provides a novel analytical solution for the Green's and transfer functions in linear perturbation theory, especially at intermediate scales relevant for BAO.

Findings

Analytical expressions for Green's and transfer functions across all scales.

Accurate modeling of BAO scales using the proposed framework.

Simplified calculations compared to numerical codes.

Abstract

In linear perturbation theory, all information about the growth of structure is contained in the Green's function, or equivalently, transfer function. These functions are generally computed using numerical codes or by phenomenological fitting formula anchored in accurate analytic results in the limits of large and small scale. Here we present a framework for analytically solving all scales, in particular the intermediate scales relevant for the baryon acoustic oscillations (BAO). We solve for the Green's function and transfer function using spherically-averaged overdensities and the approximation that the density of the coupled baryon-photon fluid is constant interior to the sound horizon.