Dark matter and halo bispectrum in redshift space: theory and applications

Abstract

Abstract. 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 ≤ 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 ∼ 5% accuracy for k i 0.10 h/Mpc at z = 0, for k i 0.15 h/Mpc at z = 0.5, for k i 0.17 h/Mpc at z = 1.0 and for k i 0.20 h/Mpc at z = 1.5. For very squeezed triangles with k 1 = k 2 0.1 hMpc −1 and k 3 ≤ 0.02 hMpc −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 Ω m , in the range 0.2 Ω m 0.4, and consequently with different values of the logarithmic grow rate f at z = 0, 0.4 f (z = 0) 0.6. We apply this new formula to recover the bias parameters, f and σ 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 σ 8 . For dark matter particles the new model can be used to recover f and σ 8 with ∼ 1% accuracy. For dark matter haloes we find that f and σ 8 present larger systematic shifts, ∼ 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 σ 8 is still recovered with ∼ 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.

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: RSD measurement from the LOS-dependent power spectrum of DR12 BOSS galaxies

“…In order to reduce the number of free bias parameters, we assume that the bias is local in Lagrangian space, which sets the values of b s 2 and b 3nl given the linear bias coefficient, b1. This assumption has been validated using Nbody simulations, and it provides consistent results between the power spectrum and bispectrum for the CMASS sample (Gil-Marín et al 2014. In case the condition of local Lagrangian bias were relaxed, the parameters b s 2 and b 3nl would be treated as free parameters, increasing, consequently, the number of free parameters of the bias model.…”

Measuring neutrino masses with large-scale structure: Euclid forecast with controlled theoretical error

“…However, the LSS data analysis is complicated by effects of non-linear clustering, galaxy bias and redshift space distortions. Our ability to fully and yield more robust constraints on cosmological parameters [37][38][39][40][41][42].…”

Position-dependent correlation function from the SDSS-III Baryon Oscillation Spectroscopic Survey Data Release 10 CMASS sample

“…While we restrict to the local bias model and the tree-level bispectrum, ref. [16] includes a non-local tidal bias [31][32][33] and uses more sophisticated bispectrum modeling using the effective F 2 kernel [34,35]. In appendix B, we show that using the effective F 2 kernel and the non-local tidal bias in the model increases the value of b 2 , but the changes are well within the 1-σ uncertainties.…”

“…Their model replaces F 2 and G 2 in eq. (2.21) with "effective" kernels, F eff 2 [34] and G eff 2 [35], which are calibrated to match the nonlinear matter bispectrum in of N-body simulations. Their model also adds a non-local galaxy bias caused by tidal fields [31][32][33] to Z 2 , i.e.,…”