Cosmological information in the redshift-space bispectrum

TL;DR

This study assesses whether the galaxy bispectrum in redshift space provides additional cosmological insights beyond the power spectrum, finding moderate improvements that are limited when combined with CMB priors, and emphasizing the importance of binning strategies.

Contribution

It derives a generalized expression for the bispectrum and its covariance with the power spectrum, considering binning effects and the monopole approximation, to evaluate their combined cosmological constraining power.

Findings

Bispectrum and power spectrum provide similar constraints individually.

Combining both reduces parameter uncertainties by a factor of 2.6.

No significant benefit when combined with current CMB priors.

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.