The key to precise and accurate cosmology: Simulating the physics that shapes gaseous haloes

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Observational programs aimed at mapping the large-scale structure of the Universe, such as eROSITA and Euclid, are ushering in the era of Precision Cosmology. Our knowledge will soon transition from being limited by statistical errors, to being hindered by systematic uncertainties. These systematics arise from the theoretical modeling adopted to fit the data and the complex physics of galaxy formation, whose effects are often neglected. In fact, powerful feedback processes from supermassive black holes (SMBHs) affect the phase-space and thermodynamical properties of the gas within haloes and beyond, in turn modifying the expectations for the cosmological observables and the large-scale matter distribution. In order to fulfill the potential of observational cosmology, we must take a far-reaching step forward by a) designing novel types of large-scale simulations that model gaseous haloes and the effects of SMBH feedback to unprecedented levels of realism and by b) providing quantitative and trustworthy — that is, physically-motivated and observationally-validated — prescriptions for cosmological analyses. Starting from the well-validated IllustrisTNG hydrodynamical simulations, we will extend their scope to more massive systems with a new suite, TNG-Cluster. We will provide a library of baryon-informed formulae for cosmological constraints with galaxies, groups, and clusters as well as design novel observational tests for SMBH feedback models. Going beyond the state-of-the-art, we will develop numerical models that account for the effects of the multi-phase structure of the gas, of radiation, and of more sophisticated SMBH physics by using new simulation techniques and by complementing the AREPO code with on-the-fly machine learning-based methods. These will enable groundbreaking large-scale simulations, new types of comparisons to observations of both the hot and cold halo gas, and, ultimately, novel and independent analyses of available cosmological data.