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

Understand

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 $S_8\times\Omega_m$.