Equivalence principle and the baryon acoustic peak

Abstract

We study the dominant effect of a long wavelength density perturbation $\ensuremath{\delta}({\ensuremath{\lambda}}_{L})$ on short distance physics. In the nonrelativistic limit, the result is a uniform acceleration, fixed by the equivalence principle, and typically has no effect on statistical averages due to translational invariance. This same reasoning has been formalized to obtain a ``consistency condition'' on the cosmological correlation functions. In the presence of a feature, such as the acoustic peak at ${\ensuremath{\ell}}_{\mathrm{BAO}}$, this naive expectation breaks down for ${\ensuremath{\lambda}}_{L}<{\ensuremath{\ell}}_{\mathrm{BAO}}$. We calculate a universal piece of the three-point correlation function in this regime. The same effect is shown to underlie the spread of the acoustic peak, and is calculable to all orders in the long modes. This can be used to improve the result of perturbative calculations---a technique known as ``infra-red resummation''---and is explicitly applied to the one-loop calculation of the power spectrum. Finally, the success of baryon acoustic oscillation reconstruction schemes is argued to be another empirical evidence for the validity of the results.