  We study the cosmological information content of the redshift-space galaxy
bispectrum monopole at one-loop order in perturbation theory. We incorporate
all effects necessary for comparison to data: fourth-order galaxy bias,
infrared resummation (accounting for the non-linear evolution of baryon
acoustic oscillations), ultraviolet counterterms, non-linear redshift-space
distortions, stochastic contributions, projection, and binning effects. The
model is implemented using FFTLog, and validated with the PT Challenge suite of
$N$-body simulations, whose large volume allows for high-precision tests.
Focusing on the mass fluctuation amplitude, $\sigma_8$, and galaxy bias
parameters, we find that including one-loop corrections allow us to
significantly extend the range of scales over which the bispectrum can be
modeled, and greatly tightens constraints on bias parameters. However, this
does not lead to noticeable improvements in the $\sigma_8$ errorbar due to the
necessary marginalization over a large number of nuisance parameters with
conservative priors. Analyzing a BOSS-volume likelihood, we find that the
addition of the one-loop bispectrum may lead to improvements on primordial
non-Gaussianity constraints by $\lesssim 30\%$ and on $\sigma_8$ by $\approx
10\%$, though we caution that this requires pushing the analysis to short
scales where the galaxy bias parameters may not be correctly recovered; this
may lead to biases in the recovered parameter values. We conclude that
restrictive priors from simulations or higher-order statistics such as the
bispectrum multipoles will be needed in order to realize the full information
content of the galaxy bispectrum.
