Nonlinear Behavior of Baryon Acoustic Oscillations from the Zel'dovich
  Approximation Using a Non-Fourier Perturbation Approach
  Baryon acoustic oscillations are an excellent technique to constrain the
properties of dark energy in the Universe. In order to accurately characterize
the dark energy equation of state, we must understand the effects of both the
nonlinearities and redshift space distortions on the location and shape of the
acoustic peak. In this paper, we consider these effects using the Zel'dovich
approximation and a novel approach to 2nd order perturbation theory. The second
order term of the Zel'dovich power spectrum is built from convolutions of the
linear power spectrum with polynomial kernels in Fourier space, suggesting that
the corresponding term of the the Zel'dovich correlation function can be
written as a sum of quadratic products of a broader class of correlation
functions, expressed through simple spherical Bessel transforms of the linear
power spectrum. We show how to systematically perform such a computation. We
explicitly prove that our result is the Fourier transform of the Zel'dovich
power spectrum, and compare our expressions to numerical simulations. Finally,
we highlight the advantages of writing the nonlinear expansion in configuration
space, as this calculation is easily extended to redshift space, and the higher
order terms are mathematically simpler than their Fourier counterparts.
