This work and its companion paper, Amon et al. [Phys. Rev. D 105, 023514 (2022)], present cosmic shear measurements and cosmological constraints from over 100 million source galaxies in the Dark Energy Survey (DES) Year 3 data. We constrain the lensing amplitude parameter S 8 ≡ σ 8 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ω m =0.3 p at the 3% level in ΛCDM: S 8 ¼ 0.759 þ0.025 −0.023 (68% CL). Our constraint is at the 2% level when using angular scale cuts that are optimized for the ΛCDM analysis: S 8 ¼ 0.772 þ0.018 −0.017 (68% CL). With cosmic shear alone, we †

Measurements of the linear growth factor D at different redshifts z are key to distinguish among cosmological models. One can estimate the derivative dD(z)/d ln(1 + z) from redshift space measurements of the 3D anisotropic galaxy two-point correlation ξ(z), but the degeneracy of its transverse (or projected) component with galaxy bias, introduces large errors in the growth measurement.Here we present a comparison between two methods which break this degeneracy by combining second-and third-order statistics. One uses the shape of the reduced three-point correlation and the other a combination of third-order one-and two-point cumulants. These methods use the fact that, for Gaussian initial conditions and scales larger than 20 h −1 Mpc, the reduced third-order matter correlations are independent of redshift (and therefore of the growth factor) while the third-order galaxy correlations depend on b. We use matter and halo catalogs from the MICE-GC simulation to test how well we can recover b(z) and therefore D(z) with these methods in 3D real space. We also present a new approach, which enables us to measure D directly from the redshift evolution of second-and third-order galaxy correlations without the need of modelling matter correlations.For haloes with masses lower than 10 14 h −1 M ⊙ , we find 10% deviations between the different estimates of D, which are comparable to current observational errors. At higher masses we find larger differences that can probably be attributed to the breakdown of the bias model and non-Poissonian shot noise.

Using a dark matter simulation we show how halo bias is determined by local density and not by halo mass. This is not totally surprising as, according to the peak-background split model, local matter density (δ) is the property that constrains bias at large scales. Massive haloes have a high clustering because they reside in high density regions. Small haloes can be found in a wide range of environments which determine their clustering amplitudes differently. This contradicts the assumption of standard Halo Occupation Distribution (HOD) models that the bias and occupation of haloes is determined solely by their mass. We show that the bias of central galaxies from semi-analytic models of galaxy formation as a function of luminosity and colour is therefore not correctly predicted by the standard HOD model. Usinḡ δ (of matter or galaxies) instead of halo mass the HOD model correctly predicts galaxy bias. These results indicate the need to include information about local density and not only mass in order to correctly apply HOD analysis in these galaxy samples. This new model can be readily applied to observations and has the advantage that the galaxy density can be directly observed, in contrast with the dark matter halo mass.

We study the linear and non-linear bias parameters which determine the mapping between the distributions of galaxies and the full matter density fields, comparing different measurements and predictions. Associating galaxies with dark matter haloes in the MICE Grand Challenge N-body simulation we directly measure the bias parameters by comparing the smoothed density fluctuations of haloes and matter in the same region at different positions as a function of smoothing scale. Alternatively we measure the bias parameters by matching the probability distributions of halo and matter density fluctuations, which can be applied to observations. These direct bias measurements are compared to corresponding measurements from two-point and different third-order correlations, as well as predictions from the peak-background model, which we presented in previous articles using the same data. We find an overall variation of the linear bias measurements and predictions of ∼ 5% with respect to results from two-point correlations for different halo samples with masses between ∼ 10 12 − 10 15 h −1 M ⊙ at the redshifts z = 0.0 and 0.5. Variations between the second-and thirdorder bias parameters from the different methods show larger variations, but with consistent trends in mass and redshift. The various bias measurements reveal a tight relation between the linear and the quadratic bias parameters, which is consistent with results from the literature based on simulations with different cosmologies. Such a universal relation might improve constraints on cosmological models, derived from second-order clustering statistics at small scales or higher-order clustering statistics.