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Baryon acoustic oscillations are an excellent technique to constrain theproperties of dark energy in the Universe. In order to accurately characterizethe dark energy equation of state, we must understand the effects of both thenonlinearities and redshift space distortions on the location and shape of theacoustic peak. In this paper, we consider these effects using the Zel'dovichapproximation and a novel approach to 2nd order perturbation theory. The secondorder term of the Zel'dovich power spectrum is built from convolutions of thelinear power spectrum with polynomial kernels in Fourier space, suggesting thatthe corresponding term of the the Zel'dovich correlation function can bewritten as a sum of quadratic products of a broader class of correlationfunctions, expressed through simple spherical Bessel transforms of the linearpower spectrum. We show how to systematically perform such a computation. Weexplicitly prove that our result is the Fourier transform of the Zel'dovichpower spectrum, and compare our expressions to numerical simulations. Finally,we highlight the advantages of writing the nonlinear expansion in configurationspace, as this calculation is easily extended to redshift space, and the higherorder terms are mathematically simpler than their Fourier counterparts.

Nonlinear Behavior of Baryon Acoustic Oscillations from the Zel'dovich Approximation Using a Non-Fourier Perturbation Approach