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The Hubble tension refers to the discrepancy in the value of the Hubbleconstant $H_0$ inferred from the cosmic microwave background observations,assuming the concordance $\Lambda$CDM model of the Universe, and that from thedistance ladder and other direct measurements. In order to alleviate thistension, we construct a plausible dark energy scenario, within the framework ofHorndeski gravity which is one of the most general scalar-tensor theoriesyielding second-order equations. In our set-up, we include theself-interactions and nonminimal coupling of the dynamical dark energy scalarfield which enable very interesting dynamics leading to a phantom behaviour atlow redshifts along with negative dark energy densities at high redshifts.These two features together make this model a promising scenario to alleviatethe Hubble tension for appropriate choices of the model parameters. Towards aconsistent model building, we show that this set-up is also free from both thegradient and ghost instabilities. Finally, we confront the predictions of themodel with low redshift observations from Pantheon, SH0ES, cosmic chronometersand BAO, to obtain best fit constraints on model parameters.

Towards a possible solution to the Hubble tension with Horndeski gravity