The present spatial distribution of galaxies in the Universe is non-Gaussian, with 40% skewness in 50 h −1 Mpc spheres, and remarkably little is known about the information encoded in it about cosmological parameters beyond the power spectrum. In this work we present an attempt to bridge this gap by studying the bispectrum, paying particular attention to a joint analysis with the power spectrum and their combination with CMB data. We address the covariance properties of the power spectrum and bispectrum including the effects of beat coupling that lead to interesting cross-correlations, and discuss how baryon acoustic oscillations break degeneracies. We show that the bispectrum has significant information on cosmological parameters well beyond its power in constraining galaxy bias, and when combined with the power spectrum is more complementary than combining power spectra of different samples of galaxies, since non-Gaussianity provides a somewhat different direction in parameter space. In the framework of flat cosmological models we show that most of the improvement of adding bispectrum information corresponds to parameters related to the amplitude and effective spectral index of perturbations, which can be improved by almost a factor of two. Moreover, we demonstrate that the expected statistical uncertainties in σ8 of a few percent are robust to relaxing the dark energy beyond a cosmological constant.

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The greatest challenge in the interpretation of galaxy clustering data from any surveys is galaxy bias. Using a simple Fisher matrix analysis, we show that the bispectrum provides an excellent determination of linear and non-linear bias parameters of intermediate and high-z galaxies, when all measurable triangle configurations down to mildly non-linear scales, where perturbation theory is still valid, are included. The bispectrum is also a powerful probe of primordial non-Gaussianity. The planned galaxy surveys at z 2 should yield constraints on non-Gaussian parameters, f loc.N L and f eq. N L , that are comparable to, or even better than, those from CMB experiments. We study how these constraints improve with volume, redshift range, as well as the number density of galaxies. Finally, we show that a halo occupation distribution may be used to improve these constraints further by lifting degeneracies between gravity, bias, and primordial non-Gaussianity.

We use a large suite of N-body simulations to study departures from universality in halo abundances and clustering in cosmologies with non-vanishing neutrino masses. To this end, we study how the halo mass function and halo bias factors depend on the scaling variable σ 2 (M, z), the variance of the initial matter fluctuation field, rather than on halo mass M and redshift z themselves. We show that using the variance of the cold dark matter rather than the total mass field, i.e., σ 2 cdm (M, z) rather than σ 2 m (M, z), yields more universal results. Analysis of halo bias yields similar conclusions: When large-scale halo bias is defined with respect to the cold dark matter power spectrum, the result is both more universal, and less scale-or k-dependent. These results are used extensively in Papers I and III of this series.