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Feedback from active galactic nuclei and stellar processes changes the matterdistribution on small scales, leading to significant systematic uncertainty inweak lensing constraints on cosmology. We investigate how the observableproperties of group-scale halos can constrain feedback's impact on the matterdistribution using Cosmology and Astrophysics with MachinE Learning Simulations(CAMELS). Extending the results of previous work to smaller halo masses andhigher wavenumber, $k$, we find that the baryon fraction in halos containssignificant information about the impact of feedback on the matter powerspectrum. We explore how the thermal Sunyaev Zel'dovich (tSZ) signal fromgroup-scale halos contains similar information. Using recent Dark Energy Survey(DES) weak lensing and Atacama Cosmology Telescope (ACT) tSZ cross-correlationmeasurements and models trained on CAMELS, we obtain $10\%$ constraints onfeedback effects on the power spectrum at $k \sim 5\, h/{\rm Mpc}$. We showthat with future surveys, it will be possible to constrain baryonic effects onthe power spectrum to $\mathcal{O}(<1\%)$ at $k = 1\, h/{\rm Mpc}$ and$\mathcal{O}(3\%)$ at $k = 5\, h/{\rm Mpc}$ using the methods that we introducehere. Finally, we investigate the impact of feedback on the matter bispectrum,finding that tSZ observables are highly informative in this case.

Inferring the impact of feedback on the matter distribution using the Sunyaev Zel'dovich effect: Insights from CAMELS simulations and ACT+DES data