Minimizing the impact of scale-dependent galaxy bias on the joint cosmological analysis of large-scale structures

Abstract

We present a mitigation strategy to reduce the impact of non-linear galaxy bias on the joint ‘3 × 2pt’ cosmological analysis of weak lensing and galaxy surveys. The Ψ-statistics that we adopt are based on Complete Orthogonal Sets of E/B Integrals. As such they are designed to minimize the contributions to the observable from the smallest physical scales where models are highly uncertain. We demonstrate that Ψ-statistics carry the same constraining power as the standard two-point galaxy clustering and galaxy–galaxy lensing statistics, but are significantly less sensitive to scale-dependent galaxy bias. Using two galaxy bias models, motivated by halo model fits to data and simulations, we quantify the error in a standard 3 × 2pt analysis where constant galaxy bias is assumed. Even when adopting conservative angular scale cuts, that degrade the overall cosmological parameter constraints, we find of order 1σ biases for Stage III surveys on the cosmological parameter S8 = σ8(Ωm/0.3)α. This arises from a leakage of the smallest physical scales to all angular scales in the standard two-point correlation functions. In contrast, when analysing Ψ-statistics under the same approximation of constant galaxy bias, we show that the bias on the recovered value for S8 can be decreased by a factor of ∼2, with less conservative scale cuts. Given the challenges in determining accurate galaxy bias models in the highly non-linear regime, we argue that 3 × 2pt analyses should move towards new statistics that are less sensitive to the smallest physical scales.

KiDS-1000 Cosmology: Multi-probe weak gravitational lensing and spectroscopic galaxy clustering constraints

“…Analysing these IA halo-models with the NLA model, they find the highest NLA model amplitude of A IA = 0.44 ± 0.13 when adopting a broken power-law for the red-central luminosity scaling. This is consistent with the Asgari et al (2021b) KiDS-1000 COSEBIs cosmic shear constraints with A IA = 0.26 +0.42 −0.34 , the KiDS-1000 band power cosmic shear constraints with A IA = 0.97 +0.29 −0.38 and the KiDS-1000 3 × 2 pt band power constraints with A IA = 1.07 +0.27 −0.31 , with the largest 1.9σ difference found for the 3 × 2 pt results.…”

“…The erroneous increase in b 1 leads to a decrease in the recovered S 8 , and also an overall reduction in the goodness-of-fit of the model with χ 2 MAP = 379.8 for ∼300 degrees of freedom. This result should serve as a point of caution for 3 × 2 pt analyses that adopt an effective linear bias model (see also the discussion in Asgari et al 2021b), although we note that our analysis is particularly sensitive to the galaxy bias model given the high signal-to-noise BOSS clustering observations that probe physical scales as low as s min = 20 h −1 Mpc. 6, comparing the fiducial 3 × 2 pt analysis (red) to a selection of our sensitivity test analyses where we ignore the impact of baryon feedback (the 'No baryon' case, sea-green), limit the analysis to a linear galaxy bias model (the 'No higher order GC' case, lime-green), and remove individual tomographic bins from our weak lensing observables (orange, purple and pink).…”

“…( 2). No matter which -scales we restrict our analysis to, high-k scales will contribute to all angular scales at some level (Joachimi et al 2021;Asgari et al 2021b). This approach also decreases the compute time of the galaxygalaxy lensing likelihood evaluations, by several orders of magnitude, in comparison to the direct perturbative calculation.…”

“…signal contaminated by the range of different IA halo models allowed by observations, Fortuna et al (2021) conclude that the redshift dependence of the true IA halo model is not large enough to bias the cosmological parameters in a KiDS-like cosmic shear analysis with the NLA model. Asgari et al (2021b) nevertheless explore one extension of the NLA model, with the inclusion of a redshift-dependent scaling term, which does not change the recovered KiDS-1000 cosmic shear MAP S 8 value.…”

Consistency of cosmic shear analyses in harmonic and real space

“…That information likely lies within the particular k modes that are captured by one statistics and missed by the other, as discussed in the introduction. An alternative is to use other statistics that exploit information from both spaces, such as COSEBIs or -and ϒ-statistics (Asgari et al 2020a), at the cost of increased complexity in estimation from data and modelling from theory.…”