Baryon-free $S_8$ tension with Stage IV cosmic shear surveys

Abstract: Accurately modelling matter power spectrum effects at small scales, such as baryonic feedback, is essential to avoid significant bias in the estimation of cosmological parameters with cosmic shear. However, Stage IV surveys like LSST will be so precise that significant information can still be extracted from large scales alone. In this work, we simulate LSST Y1-like mock data and perform a cosmic shear analysis, considering different models of baryonic feedback. To focus on large scales, we apply physically motivated scale cuts which account for the redshift dependence of the multipoles in the tomographic bin. Our main focus is to study the changes in the constraining power of $S_8$ and $\Omega_m$ parameters and assess possible effects on the tension with Planck measurements. We find that the $S_8$ tension is clearly detectable at $k_{\rm eff}^{\rm max}=0.20\,h\rm Mpc^{-1}$ in the analysis where we imposed a DES-sized tension, and at $k_{\rm eff}^{\rm max}=0.10\,h\rm Mpc^{-1}$ with a KiDS-sized tension, regardless of whether an incorrect model for baryons is assumed. However, to achieve these results, LSST will need high precision measurement of the redshift distributions, with photo-$z$ biases of the order of $10^{-3}$. Without this, the ability to constrain cosmological parameters independently of baryonic feedback - particularly regarding the $S_8$ tension - will be compromised.