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]