Holographic Boundary Conformal Field Theory within Horndeski Gravity

We investigate entanglement islands and the Page curve in the framework of Horndeski gravity on a Karch-Randall braneworld background. In particular, treating the holographic boundary conformal field theory analytically we find that the Horndeski parameters significantly alter the behavior of the Page curve compared to standard general relativity, a feature caused by the nontrivial geometry induced by the Horndeski scalar field. Interestingly enough, the geometry far from the AdS limit plays a more significant role compared to previous studies. This suggests that Horndeski gravity introduces important modifications to the distribution of quantum information in the holographic model. Finally, we claim that holographic consistency can be used reversely to impose constraints on Horndeski gravity itself, providing a new tool for probing the validity of modified gravity theories.