Alleviating $H_0$ tension in Horndeski gravity

We show that the $H_0$ tension can be alleviated in the framework of Horndeski/generalized galileon gravity. In particular, since the terms depending on $G_5$ control the friction in the Friedmann equation, we construct specific sub-classes in which it depends only on the field's kinetic energy. Since the latter is small at high redshifts, namely at redshifts which affected the CMB structure, the deviations from $Λ$CDM cosmology are negligible, however as time passes it increases and thus at low redshifts the Hubble function acquires increased values in a controlled way. We consider two Models, one with quadratic and one with quartic dependence on the field's kinetic energy. In both cases we show the alleviation of the tension, resulting to $H_0 \approx 74$ km/s/Mpc for particular parameter choices. Finally, we examine the behavior of scalar metric perturbations, showing that the conditions for absence of ghost and Laplacian instabilities are fulfilled throughout the evolution, and we confront the models with SNIa data.

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