## Amplitude of matter perturbations with SO

Simons Observatory aims to measure the amplitude of matter perturbations, σ8, out to z = 4 with a 2% constraint between z = 1–2 in three ways: (i) SZ galaxy clusters calibrated with LSST weak lensing; (ii) SZ galaxy clusters calibrated with SO CMB lensing measurements; (iii) CMB lensing maps cross-correlated with the LSST galaxy number density in tomographic redshift bins.

Figure (1) shows the relative uncertainty on σ8, defined in six tomographic redshift bins (z=0–0.5, 0.5–1, 1–2, 2–3, 3–4, 4–7), as a function of redshift. The forecast assumes a joint analysis of Cκκ, Cκg and Cgg, where κ is SO CMB lensing and g denotes LSST galaxies binned in tomographic redshift bins. Planck CMB information — with a τ prior, σ(τ) = 0.01 — and BAO measurements (DESI forecast) are also included. The filled bands and single lines distinguish between an SO survey over sky fractions fsky = 0.4 and 0.1, respectively. Different colors distinguish between the SO baseline and goal configurations, and for this latter case different LSST number density, for the gold and optimistic sample, respectively.

Figure (2) shows the uncertainty on σ8(z) for various redshift bins obtained from the abundances of SO-detected SZ clusters calibrated using CMB halo lensing.

## The Hubble constant from SO

Simons Observatory aims to reduce the current uncertainty on the Hubble constant derived from the primary CMB within the ΛCDM model, reaching a half-percent measurement on H0.

Figure (3) shows constraints on the Hubble constant in a ΛCDM model from different SO high-multipole channels and the full SO baseline dataset (purple and blue bars), compared to the current estimate provided by Planck (TT,TT,EE+lowE+lensing) and the recent local measurement from the SH0ES project. The SO forecasts are centered on a fiducial value of H0 = 70 km/s/Mpc, i.e, the mean value between the Planck and the SH0ES measurements.