Abstract
We investigate the impact of different assumptions in the modeling of one-loop galaxy bias on the recovery of cosmological parameters, as a follow up of the analysis done in the first paper of the series at fixed cosmology. We use three different synthetic galaxy samples whose clustering properties match the ones of the CMASS and LOWZ catalogues of BOSS and the SDSS Main Galaxy Sample. We investigate the relevance of allowing for either short range non-locality or scale-dependent stochasticity by fitting the real-space galaxy auto power spectrum or the combination of galaxy-galaxy and galaxy-matter power spectrum. From a comparison among the goodness-of-fit ($\chi^2$), unbiasedness of cosmological parameters (FoB), and figure-of-merit (FoM), we find that a four-parameter model (linear, quadratic, cubic non-local bias, and constant shot-noise) with fixed quadratic tidal bias provides a robust modelling choice for the auto power spectrum of the three samples, up to $k_{\rm max}=0.3\,h\,\mathrm{Mpc}^{-1}$ and for an effective volume of $6\,h^{-3}\,\mathrm{Gpc}^3$. Instead, a joint analysis of the two observables fails at larger scales, and a model extension with either higher derivatives or scale-dependent shot-noise is necessary to reach a similar $k_{\rm max}$, with the latter providing the most stable results. These findings are obtained with three, either hybrid or perturbative, prescriptions for the matter power spectrum, \texttt{RESPRESSO}, gRPT and EFT. In all cases, the inclusion of scale-dependent shot-noise increases the range of validity of the model in terms of FoB and $\chi^2$. Interestingly, these model extensions with additional free parameters do not necessarily lead to an increase in the maximally achievable FoM for the cosmological parameters $\left(h,\,\Omega_ch^2,\,A_s\right)$, which are generally consistent to those of the simpler model at smaller $k_{\rm max}$.
Highlights
Over the past decades galaxy redshift surveys have provided a wealth of information on the large-scale distribution of galaxies across the Universe
We measured both observables from a set of three different synthetic galaxy samples, whose clustering properties are meant to reproduce the ones of three real data catalogs, i.e. CMASS and LOWZ from BOSS, and Main Galaxy Sample (MGS) from SDSS
The analytical recipes we adopted to model these observables are based on a standard one-loop expansion of the galaxy density field on the matter density field, collecting terms related to both spherically symmetric gravitational collapse and tidal fields up to third order in perturbations
Summary
Include higher powers At the same time it has of δ, been shown that anisotropies in the process of gravitational collapse are responsible for the generation of non-negligible tidal effects, which contribute to the local distribution of galaxies [15,16] This finding followed the realization that the local-in-matter-density bias model had limitations in providing a proper description of the clustering of dark matter halos [17,18] and was leading to incompatible constraints on the quadratic bias b2 from measurements of the power spectrum and bispectrum [19,20].
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