### Abstract

Gravitational clustering is an intrinsically nonlinear process that generates significant non-Gaussian signatures in the density field. We consider how these affect power spectrum determinations from galaxy and weak-lensing surveys. Non-Gaussian effects not only increase the individual error bars compared to the Gaussian case but, most importantly, lead to nontrivial cross-correlations between different band powers, correlating small-scale band powers both among themselves and with those at large scales. We calculate the power-spectrum covariance matrix in nonlinear perturbation theory (weakly nonlinear regime), in the hierarchical model (strongly nonlinear regime), and from numerical simulations in real and redshift space. In particular, we show that the hierarchical Ansatz cannot be strictly valid for the configurations of the trispectrum involved in the calculation of the power-spectrum covariance matrix. We discuss the impact of these results on parameter estimation from power-spectrum measurements and their dependence on the size of the survey and the choice of band powers. We show that the non-Gaussian terms in the covariance matrix become dominant for scales smaller than the nonlinear scale k_{nl} ∼ 0.2 h^{-1} Mpc^{-1}, depending somewhat on power normalization. Furthermore, we find that cross-correlations mostly deteriorate the determination of the amplitude of a rescaled power spectrum, whereas its shape is less affected. In weak lensing surveys the projection tends to reduce the importance of non-Gaussian effects. Even so, for background galaxies at redshift z ∼ 1, the non-Gaussian contribution rises significantly around l ∼ 1000 and could become comparable to the Gaussian terms depending upon the power spectrum normalization and cosmology. The projection has another interesting effect: the ratio between non-Gaussian and Gaussian contributions saturates and can even decrease at small enough angular scales if the power spectrum of the three-dimensional field falls faster than k^{-2}.

Original language | English (US) |
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Pages (from-to) | 1-15 |

Number of pages | 15 |

Journal | Astrophysical Journal |

Volume | 527 |

Issue number | 1 PART 1 |

DOIs | |

State | Published - Dec 10 1999 |

### Keywords

- Galaxies: clusters: general
- Large-scale structure of universe
- Methods: numerical
- Methods: statistical

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

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## Cite this

*Astrophysical Journal*,

*527*(1 PART 1), 1-15. https://doi.org/10.1086/308059