Reconstructing the shape of the non-linear matter power spectrum using CMB lensing and cosmic shear

We reconstruct the non-linear matter power spectrum $P(k)$ using a joint analysis of gravitational lensing of the cosmic microwave background (CMB) and lensing of galaxies. This reconstruction is motivated by the $S_8$ tension between early-universe CMB predictions and late-time observables. We use CMB lensing data from the Atacama Cosmology Telescope DR6 and cosmic shear data from the Dark Energy Survey (DES) Y3 release to perform a gravity-only (i.e. no baryonic feedback) fit to $P(k)$ in bins of wave-number, within $\rm{\Lambda CDM}$. We find that with DES cosmic shear data alone, $P(k)$ departs from the early-universe CMB prediction on all scales. The joint fit with CMB lensing is consistent on large scales $k<0.2 \;{\rm Mpc}^{-1}$ but shows a $\sim 2 \sigma$ deviation from scale-independence when extending to $k = 10 \;h/\mathrm{Mpc}$. We compare our agnostic $P(k)$ reconstruction to baryonic feedback models and non-standard dark matter models: reasonable variations of both scenarios can recover the shape and amplitude of the suppression. We discuss the advances needed to disentangle these physical effects with a full mapping of $P(k,z)$.