Loop Corrections in Nonlinear Cosmological Perturbation Theory. II. Two‐Point Statistics and Self‐Similarity

Abstract

We calculate the lowest-order non-linear contributions to the power spectrum, two-point correlation function, and smoothed variance of the density field, for Gaussian initial conditions and scale-free initial power spectra, $P(k) \sim k^n$. These results extend and in some cases correct previous work in the literature on cosmological perturbation theory. Comparing with the scaling behavior observed in N-body simulations, we find that the validity of non-linear perturbation theory depends strongly on the spectral index $n$. For $n < -1$, the power spectrum, variance, and correlation function in the scaling regime can be calculated using dimensional regularization.