### 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) |
---|---|

Pages (from-to) | 620-644 |

Number of pages | 25 |

Journal | Astrophysical Journal |

Volume | 473 |

Issue number | 2 PART I |

DOIs | |

State | Published - 1996 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

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

**Loop corrections in nonlinear cosmological perturbation theory. II. two-point statistics and self-similarity.** / Scoccimarro, Román; Frieman, Joshua A.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 473, no. 2 PART I, pp. 620-644. https://doi.org/10.1086/178177

}

TY - JOUR

T1 - Loop corrections in nonlinear cosmological perturbation theory. II. two-point statistics and self-similarity

AU - Scoccimarro, Román

AU - Frieman, Joshua A.

PY - 1996

Y1 - 1996

N2 - 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) ∼ kn. 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 σ2(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.

AB - 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) ∼ kn. 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 σ2(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.

KW - Galaxies: clusters: general

KW - Large-scale structure of universe

KW - Methods: Numerical

UR - http://www.scopus.com/inward/record.url?scp=26144480068&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26144480068&partnerID=8YFLogxK

U2 - 10.1086/178177

DO - 10.1086/178177

M3 - Article

VL - 473

SP - 620

EP - 644

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 2 PART I

ER -