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.
CITATION STYLE
Scoccimarro, R., & Frieman, J. A. (1996). Loop Corrections in Nonlinear Cosmological Perturbation Theory. II. Two‐Point Statistics and Self‐Similarity. The Astrophysical Journal, 473(2), 620–644. https://doi.org/10.1086/178177
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