Towards a possible solution to the Hubble tension with Horndeski gravity

The Hubble tension refers to the discrepancy in the value of the Hubble constant H_0 inferred from the cosmic microwave background observations, assuming the LambdaCDM model of the universe, and that from the distance ladder and other direct measurements. In order to alleviate this tension, we construct a plausible dark energy scenario, within the framework of Horndeski gravity which is one of the most general scalar-tensor theories yielding second-order equations. In our set-up, we include the self-interactions and nonminimal coupling of the dynamical dark energy scalar field which enable very interesting dynamics leading to a phantom behaviour at low redshifts along with negative dark energy densities at high redshifts. These two features together make this model a promising scenario to alleviate the Hubble tension for appropriate choices of the model parameters. Finally, as a consistency check, we show that this set-up is also free from the gradient and ghost instabilities.