Role of the Hubble Scale in the Weak Lensing vs. CMB Tension

TL;DR

This paper investigates the role of the Hubble scale in the tension between weak lensing and CMB data, proposing a new parameterization and analyzing its implications for resolving the Hubble tension within and beyond the $\\Lambda$CDM model.

Contribution

It introduces a re-parameterization using $S_{12}$ to better understand lensing amplitude tension and explores its connection with the Hubble tension, providing scaling relations and fitting formulas.

Findings

$S_{12}$ correlates with $H_0$ in weak lensing data.

Scaling relations allow extrapolation to address tensions jointly.

Early dark energy scenario's comparison with target scalings.

Abstract

We explore a re-parameterization of the lensing amplitude tension between weak lensing (WL) and cosmic microwave background (CMB) data and its implications for a joint resolution with the Hubble tension. Specifically, we focus on the lensing amplitude over a scale of 12 Mpc in absolute distance units using a derived parameter $S_{12}$ and show its constraints from recent surveys in comparison with Planck 2018. In WL alone, we find that the absolute distance convention correlates $S_{12}$ with $H_0$. Accounting for this correlation in the 3D space $S_{12}\times \omega_m \times h$ reproduces the usual levels of $2\sim 3\sigma$ tension inferred from $S_8\times\Omega_m$. Additionally, we derive scaling relations in the $S_8\times h$ and $S_{12}\times h$ planes that are allowed by $\Lambda$CDM and extrapolate target scalings needed to solve the $H_0$ and lensing-amplitude tensions jointly in a hypothetical beyond-$\Lambda$CDM model. As a test example, we quantify how the early dark energy scenario compares with these target scalings. Useful fitting formulae for $S_8$ and $S_{12}$ as a function of other cosmological parameters in $\Lambda$CDM are provided, with 1% precision.