$H_0$ as a Universal FLRW Diagnostic

Abstract

We reverse the logic behind the apparent existence of $H_0$-tension, to design diagnostics for cosmological models. The basic idea is that the non-constancy of $H_0$ inferred from observations at different redshifts is a null hypothesis test for models within the FLRW paradigm -- if $H_0$ runs, the model is wrong. Depending on the kind of observational data, the most suitable form of the diagnostic can vary. As examples, we present two $H_0$ diagnostics that are adapted to two different BAO observables. We use these and the corresponding BAO data to Gaussian reconstruct the running of $H_0$ in flat $\Lambda$CDM with Planck values for the model parameters. For flat $\Lambda$CDM when the radiation contribution can be neglected, with comoving distance data, the diagnostic is a simple hypergeometric function. Possible late time deviations from the FLRW paradigm can also be accommodated, by simply keeping track of the (potentially anisotropic) sky variation of the diagnostic.

arXiv comment9 pages, 5 plots

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