Cosmological information in the redshift-space bispectrum

Abstract

We use the Fisher-matrix formalism to investigate whether the galaxy bispectrum in redshift space, B, contains additional cosmological information with respect to the power spectrum, P. We focus on a Euclid -like survey and consider cosmological models dominated by dark energy and cold dark matter with Gaussian primordial perturbations. After discussing the phenomenology of redshift-space distortions for the bispectrum, we derive an expression for the cross-covariance between B and P at leading order in perturbation theory. Our equation generalizes previous results that did not consider binning in the orientation of wavevector triangles with respect to the line of sight. By considering Fourier modes with wavenumber k < 0.15 h Mpc −1 , we find that B and P set similar constraints on the cosmological parameters. Generally, error bars moderately improve when the two probes are combined together. For instance, the joint 68.3 per cent credible region for the parameters that describe a dynamical dark-energy equation of state shrinks by a factor of 2.6 with respect to only using the power spectrum. Regrettably, this improvement is cancelled out when the clustering analysis is combined with priors based on current studies of the cosmic microwave background. In this case, combining B and P does not give any appreciable benefit other than allowing a precise determination of galaxy bias. Finally, we discuss how results depend on the binning strategy for the clustering statistics as well as on the maximum wavenumber. We also show that only considering the bispectrum monopole leads to a significant loss of information.the nature of dark energy and dark matter, (ii) the neutrino masses, (iii) the statistical properties of primordial density fluctuations. These are the main science drivers of the planned next generation of surveys that will be conducted, for instance, with the Dark Energy Spectroscopic Instrument (DESI, DESI Collaboration et al. 2016a,b), the Euclid satellite (Laureijs et al. 2011) and the Square Kilometre Array (SKA, Maartens et al. 2015).It is customary to extract cosmological information from galaxy catalogues using the two-point correlation function or its Fourier transform, the power spectrum. Either of these functions fully characterize a zero-mean Gaussian random field. However, the galaxy distribution displays complex patterns characterized by elongated filaments, compact clusters, and volume-filling underdense regions. These features are not captured by two-point statistics that do not retain information on the phases of the Fourier modes of the galaxy distribution. Therefore, if measured with sufficient accuracy and precision, higher-order statistics like the n-point correlation functions (with n > 2) and their Fourier transforms, the polyspectra, should contain additional information.Until recently, galaxy redshift surveys could only pro-

Detecting the relativistic galaxy bispectrum

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