Running Hubble tension and a H0 diagnostic
Chethan Krishnan, E. Ó Colgáin, M. M. Sheikh-Jabbari, Tao Yang
Abstract
Hubble tension is routinely presented as a mismatch between the Hubble constant ${H}_{0}$ determined locally and a value inferred from the flat $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmology. In essence, the tension boils down to a disagreement between two numbers. Here, assuming the tension is cosmological in origin, we predict that within flat $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ there should be other inferred values of ${H}_{0}$, and that a ``running of ${H}_{0}$ with redshift'' can be expected. These additional determinations of ${H}_{0}$ may be traced to a difference between the effective equation of state (EoS) of the Universe within the Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) cosmology framework and the current standard model. We introduce a diagnostic that flags such a running of ${H}_{0}$.