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It is common to express cosmological measurements in units of h-1 Mpc. Here, we review some of the complications that originate from this practice. A crucial problem caused by these units is related to the normalization of the matter power spectrum, which is commonly characterized in terms of the linear-theory rms mass fluctuation in spheres of radius 8 h-1 Mpc, σ8. This parameter does not correctly capture the impact of h on the amplitude of density fluctuations. We show that the use of σ8 has caused critical misconceptions for both the so-called σ8 tension regarding the consistency between low-redshift probes and cosmic microwave background data and the way in which growth-rate estimates inferred from redshift-space distortions are commonly expressed. We propose to abandon the use of h-1 Mpc units in cosmology and to characterize the amplitude of the matter power spectrum in terms of σ12, defined as the mass fluctuation in spheres of radius 12 Mpc, whose value is similar to the standard σ8 for h~0.67. [ABSTRACT FROM AUTHOR]

We perform a validation of estimates of the growth rate of structure, described by the parameter combination fσ8, in modified gravity cosmologies. We consider an analysis pipeline based on the redshift-space distortion modeling of the clustering wedges statistic of the galaxy correlation function and apply it to mock catalogues of Lambda cold dark matter (ΛCDM) and the normal branch of Dvali-Gabadadze-Porrati (DGP) cosmologies. We employ a halo occupation distribution approach to construct our mocks, which we ensure resemble the CMASS sample from Baryon Oscillation Spectroscopic Survey (BOSS) in terms of the total galaxy number density and large-scale amplitude of the power spectrum monopole. We show that the clustering wedges model successfully recovers the true growth rate difference between DGP and ΛCDM, even for cases with over 40% enhancement in fσ8 compared to ΛCDM. The unbiased performance of the clustering wedges model allows us to use the growth rate values estimated from the BOSS DR12 data to constrain the crossover scale rc of DGP gravity to [rcH0]-1<0.97 (2σ) or rc>3090 Mpc/h, cutting into the interesting region of parameter space with rc ~H-10 using constraints from the growth of structure alone. [ABSTRACT FROM AUTHOR]

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. To carry out these tests we focus on the real-space galaxy-power spectrum from a set of three different synthetic galaxy samples whose clustering properties are meant to match the ones of the CMASS and LOWZ catalogs of BOSS and the SDSS Main Galaxy Sample. We investigate the relevance of allowing for either short range nonlocality or scale-dependent stochasticity by fitting the real-space galaxy autopower spectrum or the combination of galaxy-galaxy and galaxy-matter power spectrum. From a comparison among the goodness of fit (χ²), unbiasedness of cosmological parameters (FoB), and figure of merit (FoM) of the model, we find that a simple four-parameter model (linear, quadratic, cubic nonlocal bias, and constant shot noise) with fixed quadratic tidal bias provides a robust modeling choice for the autopower spectrum of the three galaxy samples, up to kmax=0.3h Mpc-1 and for an effective volume of 6h-3 Gpc³. 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 kmax, with the latter providing the most accurate and stable results. Throughout the majority of the paper, we fix the description of the nonlinear matter evolution using a hybrid perturbative-N-body approach, respresso, that was found in the first paper to be the closest performing to the measured matter spectrum. We also test the impact of different modeling assumptions based on perturbative approaches, such as galilean-invariant Renormalised Perturbation Theory (gRPT) and effective field theory (EFT). In all cases, we find the inclusion of scale-dependent shot noise to increase the range of validity of the model in terms of FoB and χ². Interestingly, these model extensions with additional free parameters do not necessarily lead to an increase in the maximally achievable FoM for the cosmological parameters (h, Ωch², As), which are generally consistent with those of the simpler model at smaller kmax. [ABSTRACT FROM AUTHOR]

We present a joint likelihood analysis of the real-space power spectrum and bispectrum measured from a variety of halo and galaxy mock catalogs. A novel aspect of this work is the inclusion of nonlinear triangle configurations for the bispectrum, made possible by a complete next-to-leading order ("one-loop") description of galaxy bias, as is already common practice for the power spectrum. Based on the goodness of fit and the unbiasedness of the parameter posteriors, we accomplish a stringent validation of this model compared to the leading order ("tree-level") bispectrum. Using measurement uncertainties that correspond to an effective survey volume of 6 (Gpc/h)³, we determine that the one-loop corrections roughly double the applicable range of scales, from ∼0.17 h/Mpc (tree level) to ∼0.3 h/Mpc. This converts into a 1.5-2x improvement on constraints of the linear bias parameter at fixed cosmology, and a 1.5-2.4x shrinkage of uncertainties on the amplitude of fluctuations As, which clearly demonstrates the benefit of extracting information from nonlinear scales despite having to marginalize over a larger number of bias parameters. Besides, our precise measurements of galaxy bias parameters up to fourth order allow for thorough comparisons to coevolution relations, showing excellent agreement for all contributions generated by the nonlocal action of gravity. Using these relations in the likelihood analysis does not compromise the model validity and is crucial for obtaining the quoted improvements on As. We also analyzed the impact of higher-derivative and scale-dependent stochastic terms, finding that for a subset of our tracers the former can boost the performance of the tree-level model with constraints on As that are only slightly degraded compared to the one-loop model. [ABSTRACT FROM AUTHOR]

We test the regime of validity of the one-loop galaxy bias for a wide variety of biased tracers. Our most stringent test asks the bias model to simultaneously match the galaxy-galaxy and galaxy-mass spectrum, using the measured nonlinear matter spectrum from the simulations to test the one-loop effects from the bias expansion alone. In addition, we investigate the relevance of short-range nonlocality and halo exclusion through higher-derivative and scale-dependent noise terms, as well as the impact of using coevolution relations to reduce the number of free fitting parameters. From comparing the validity and merit of these assumptions, we find that a four-parameter model (linear, quadratic, cubic nonlocal bias, and constant shot noise) with a fixed quadratic tidal bias provides a robust modeling choice for the auto power spectrum of the less massive halos in our set of samples and their galaxy populations [up to kmax=0.35 h/Mpc for a sample volume of 6 (Gpc/h)³]. For the more biased tracers, it is most beneficial to include scale-dependent noise. This is also the preferred option when considering combinations of the auto and cross power spectrum, which might be relevant in joint studies of galaxy clustering and weak lensing. We also test the use of perturbation theory to account for matter loops through gRPT, EFT, and the hybrid approach RESPRESSO. While all these have similar performance, we find the latter to be the best in terms of validity and recovered mean posterior values, in accordance with it being based partially on simulations. [ABSTRACT FROM AUTHOR]