  We study the information content of the angle-averaged (monopole) redshift
space galaxy bispectrum. The main novelty of our approach is the use of a
systematic tree-level perturbation theory model that includes galaxy bias, IR
resummation, and also accounts for nonlinear redshift space distortions,
binning, and projection effects. We analyze data from the PT challenge
simulations, whose cumulative volume of 566 $h^{-3}$Gpc$^3$ allows for a
precise comparison to theoretical predictions. Fitting the power spectrum and
bispectrum of our simulated data, and varying all necessary cosmological and
nuisance parameters in a consistent Markov chain Monte Carlo analysis, we find
that our tree-level bispectrum model is valid up to $k_{\max}=0.08~h{\rm
Mpc}^{-1}$ (at $z=0.61$). We also find that inclusion of the bispectrum
monopole improves constraints on cosmological parameters by $(5-15)\%$ relative
to the power spectrum. The improvement is more significant for the quadratic
bias parameters of our simulated galaxies, which we also show to deviate from
biases of the host dark matter halos at the $\sim 3\sigma$ level. Finally, we
adjust the covariance and scale cuts to match the volume of the BOSS survey,
and estimate that within the minimal $\Lambda$CDM model the bispectrum data can
tighten the constraint on the mass fluctuation amplitude $\sigma_8$ by roughly
$10\%$.
