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 \leq 1.5 .
Our model require 18 free parameters that are fitted to N-body simulations using the shapes k _ { 2 } / k _ { 1 } = 1 , 1.5 , 2.0 , 2.5 .
We find that we can describe the bispectrum of dark matter particles with \sim 5 \% accuracy for k _ { i } \lesssim 0.10 h / { Mpc } at z = 0 , for k _ { i } \lesssim 0.15 h / { Mpc } at z = 0.5 , for k _ { i } \lesssim 0.17 h / { Mpc } at z = 1.0 and for k _ { i } \lesssim 0.20 h / { Mpc } at z = 1.5 .
For very squeezed triangles with k _ { 1 } = k _ { 2 } \gtrsim 0.1 h { Mpc } ^ { -1 } and k _ { 3 } \leq 0.02 h { Mpc } ^ { -1 } , however , neither SPT nor the proposed fitting formula are able to describe the measured dark matter bispectrum with this accuracy .
We show that the fitting formula is sufficiently general that can be applied to other intermediate shapes such as k _ { 2 } / k _ { 1 } = 1.25 , 1.75 , { and } 2.25 .
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 \sim 1 \% accuracy .
For dark matter haloes we find that f and \sigma _ { 8 } present larger systematic shifts , \sim 10 \% .
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 .
In particular , the quantity f \sigma _ { 8 } is still recovered with \sim 1 \% accuracy for the particular halo population and cosmology studied .
The improvement on the modelling of the bispectrum presented in this paper will be useful for extracting information from current and future galaxy surveys .