On constraining cosmology and the halo mass function with weak gravitational lensing

Abstract

ABSTRACT The discrepancy between the weak lensing (WL) and the Planck measurements of S8 has been a subject of several studies. Assuming that residual systematics are not the cause, these studies tend to show that a strong suppression of the amplitude of the mass power spectrum P(k) in the late Universe at high k could resolve it. The WL signal at the small scale is sensitive to various effects not related to lensing, such as baryonic effects and intrinsic alignment. These effects are still poorly understood therefore the accuracy of P(k) depends on the modelling precision of these effects. A common approach for calculating P(k) relies on a halo model. Among the various components necessary for the construction of P(k) in the halo model framework, the halo mass function (HMF) is an important one. Traditionally, the HMF has been assumed to follow a fixed model, motivated by dark matter-only numerical simulations. Recent literature shows that baryonic physics, among several other factors, could affect the HMF. In this study, we investigate the impact of allowing the HMF to vary. This provides a way of testing the validity of the halo model-HMF calibration using data. In the context of the aforementioned S8 discrepancy, we find that the Planck cosmology is not compatible with the vanilla HMF for both the DES-y3 and the KiDS-1000 data. Moreover, when the cosmology and the HMF parameters are allowed to vary, the Planck cosmology is no longer in tension. The modified HMF predicts a matter power spectrum with a $\sim 25~{{\ \rm per\ cent}}$ power loss at k ∼ 1 h Mpc−1, in agreement with the recent studies that try to mitigate the S8 tension with modifications in P(k). We show that stage IV surveys will be able to measure the HMF parameters with a few per cent accuracy.