Addressing $H_0$ tension by means of VCDM

In this letter we propose a reduction of the $H_0$ tension puzzle by means of a theory of minimally modified gravity which is dubbed VCDM. After confronting the theory with the experiments, we find that the data allow for a low-redshift transition in the expansion history of the universe at either $z\simeq 0.3$ or $z \simeq 1.8\,$, corresponding to one of the two local minima of the total $\chi^2$. From the bestfit values the total fitness parameter is improved by $\Delta \chi^2 \simeq 12$, for the data set considered. We then infer the local Hubble expansion rate today within this theory by means of low redshift Pantheon data. The resulting local Hubble expansion rate today is $H^{\rm{loc}}_0=73.6\pm1.4$. We find the tension is reduced within the VCDM theory.