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The thermal Sunyaev-Zeldovich effect contains information about the thermalhistory of the universe, observable in maps of the Compton $y$ parameter;however, it does not contain information about the redshift of the sources.Recent papers have utilized a tomographic approach, cross-correlating theCompton $y$ map with the locations of galaxies with known redshift, in order todeproject the signal along the line of sight. In this paper, we test thevalidity and accuracy of this tomographic approach to probe the thermal historyof the universe. We use the state-of-the-art cosmological hydrodynamicalsimulation, Magneticum, for which the thermal history of the universe is aknown quantity. The key ingredient is the Compton-$y$-weighted halo bias,$b_y$, computed from the halo model. We find that, at redshifts currentlyavailable, the method reproduces the correct mean thermal pressure (or thedensity-weighted mean temperature) to high accuracy, validating and confirmingthe results of previous papers. At higher redshifts ($z\gtrsim 2.5$), there issignificant disagreement between $b_y$ from the halo model and the simulation.

physical review. d/physical review. d.

Testing the SZ-based tomographic approach to the thermal history of the  universe with pressure-density cross-correlations: Insights from the  Magneticum simulation