paper

Large-scale bias in the Universe: bispectrum method

arXiv:astro-ph/9706059 · doi:10.1093/mnras/290.4.651

Abstract

Evidence that the Universe may be close to the critical density, required for its expansion eventually to be halted, comes principally from dynamical studies of large-scale structure. These studies either use the observed peculiar velocity field of galaxies directly, or indirectly by quantifying its anisotropic effect on galaxy clustering in redshift surveys. A potential difficulty with both such approaches is that the density parameter is obtained only in the combination , if linear perturbation theory is used. The determination of the density parameter is therefore compromised by the lack of a good measurement of the bias parameter , which relates the clustering of sample galaxies to the clustering of mass. In this paper, we develop an idea of Fry (1994), using second-order perturbation theory to investigate how to measure the bias parameter on large scales. The use of higher-order statistics allows the degeneracy between and to be lifted, and an unambiguous determination of then becomes possible. We apply a likelihood approach to the bispectrum, the three-point function in Fourier space. This paper is the first step in turning the idea into a practical proposition for redshift surveys, and is principally concerned with noise properties of the bispectrum, which are non-trivial. The calculation of the required bispectrum covariances involves the six-point function, including many noise terms, for which we have developed a generating functional approach which will be of value in calculating high-order statistics in general.

12 pages, latex, 7 postscript figures included. Accepted by MNRAS. (Minor numerical typesetting errors corrected: results unchanged)

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