### Abstract

We calculate the lowest order nonlinear 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^{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 nonlinear perturbation theory depends strongly on the spectral index n. For n< -1, we find excellent agreement over scales where the variance σ^{2}(R) ≲ 10; however, for n ≥ -1, perturbation theory predicts deviations from self-similar scaling (which increase with n) not seen in numerical simulations. This anomalous scaling suggests that the principal assumption underlying cosmological perturbation theory, namely, that large-scale fields can be described perturbatively even when fluctuations are highly nonlinear on small scales, breaks down beyond leading order for spectral indices n≥ -1. For n < -1, the power spectrum, variance, and correlation function in the scaling regime can be calculated using dimensional regularization.

Original language | English (US) |
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Pages (from-to) | 620-644 |

Number of pages | 25 |

Journal | Astrophysical Journal |

Volume | 473 |

Issue number | 2 PART I |

DOIs | |

State | Published - Jan 1 1996 |

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### Keywords

- Galaxies: clusters: general
- Large-scale structure of universe
- Methods: Numerical

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

*473*(2 PART I), 620-644. https://doi.org/10.1086/178177