Dark matter and halo bispectrum in redshift space: theory and
  applications
  We present a phenomenological modification of the standard perturbation
theory prediction for the bispectrum in redshift space that allows us to extend
the model to mildly non-linear scales over a wide range of redshifts,
$z\leq1.5$. We find that we can describe the bispectrum of dark matter
particles with $\sim5%$ accuracy for $k_i\lesssim0.10\,h/{\rm Mpc}$ at $z=0$,
for $k_i\lesssim0.15\,h/{\rm Mpc}$ at $z=0.5$, for $k_i\lesssim0.17\,h/{\rm
Mpc}$ at $z=1.0$ and for $k_i\lesssim0.20\,h/{\rm Mpc}$ at $z=1.5$. We also
test that the fitting formula is able to describe with similar accuracy the
bispectrum of cosmologies with different $\Omega_m$, in the range $0.2\lesssim
\Omega_m \lesssim 0.4$, and consequently with different values of the
logarithmic grow rate $f$ at $z=0$, $0.4\lesssim f(z=0) \lesssim 0.6$. We apply
this new formula to recover the bias parameters, $f$ and $\sigma_8$, by
combining the redshift space power spectrum monopole and quadrupole with the
bispectrum monopole for both dark matter particles and haloes. We find that the
combination of these three statistics can break the degeneracy between $b_1$,
$f$ and $\sigma_8$. For dark matter particles the new model can be used to
recover $f$ and $\sigma_8$ with $\sim1%$ accuracy. For dark matter haloes we
find that $f$ and $\sigma_8$ present larger systematic shifts, $\sim10%$. The
systematic offsets arise because of limitations in the modelling of the
interplay between bias and redshift space distortions, and represent a
limitation as the statistical errors of forthcoming surveys reach this level.
Conveniently, we find that these residual systematics are mitigated for
combinations of parameters. The improvement on the modelling of the bispectrum
presented in this paper will be useful for extracting information from current
and future galaxy surveys. [abridged]
