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Loop corrections in nonlinear cosmological perturbation theory 2. Two point statistics and selfsimilarity

Feb, 1996
48 pages
Published in:
  • Astrophys.J. 473 (1996) 620
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Report number:
  • FERMILAB-PUB-96-023-A
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1996200320102017202402468
Abstract: (arXiv)
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)∼k nP(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 nn. For n<−1n<-1, we find excellent agreement over scales where the variance \sigma~2(R) \la 10; however, for n≥−1n \geq -1, perturbation theory predicts deviations from self-similar scaling (which increase with nn) not seen in numerical simulations. This anomalous scaling suggests that the principal assumption underlying cosmological perturbation theory, that large-scale fields can be described perturbatively even when fluctuations are highly non-linear on small scales, breaks down beyond leading order for spectral indices n≥−1n \geq -1. For n<−1n < -1, the power spectrum, variance, and correlation function in the scaling regime can be calculated using dimensional regularization.
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