Large-Scale Bias in the Universe: Bispectrum Method

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 use the observed peculiar velocity field of galaxies either 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 Omega_0 is obtained only in the combination beta=Omega^0.6_0/b, if linear perturbation theory is used. The determination of the density parameter Omega_0 is therefore compromised by the lack of a good measurement of the bias parameter b, which relates the clustering of sample galaxies to the clustering of mass. In this paper, we develop an idea of Fry, 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 b and Omega_0 to be lifted, and an unambiguous determination of Omega_0 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.