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

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 (COSEBIs). As such they are designed to minimise 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.