Multidimensionality of the Hubble tension: the roles of ${\Omega }_m$ and ${\omega }_c$

Abstract

The Hubble tension is inherently multidimensional, and bears important implications for parameters beyond $H_0$. We discuss the key role of the matter density parameter ${\Omega }_m$ and the physical cold dark matter density ${\omega }_c$. We argue that once ${\Omega }_m$ and the physical baryon density ${\omega }_b$ are calibrated, through Baryon Acoustic Oscillations (BAO) and/or Type Ia Supernovae (SNeIa) for ${\Omega }_m$, and via Big Bang Nucleosynthesis for ${\omega }_b$, any model raising $H_0$ requires raising ${\omega }_c$ and, under minimal assumptions, also the clustering parameter $S_8$. We explicitly verify that this behaviour holds when analyzing recent BAO and SNeIa data. We argue that a calibration of ${\Omega }_m$ as reliable and model-independent as possible should be a priority in the Hubble tension discussion, and an interesting possibility in this sense could be represented by galaxy cluster gas mass fraction measurements.

16 pages, 4 figures. v2: additional references added, clarified certain aspects of the discussion, added "Cosmology with one galaxy" and follow-up works as potential model-independent probes of Omega_m. v3: added minor clarifications. Version accepted for publication in PRD

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