A simple analytic treatment of linear growth of structure with baryon acoustic oscillations

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.