Cosmological information in the redshift-space bispectrum
  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.
