Fab-Four cosmography to tackle the Hubble tension

In the context of the Fab-Four theory of gravity in a Friedmann-Lemaître-Robertson-Walker background, in this work we use the cosmography approach to study a particular self-tuning filter solution focused on a zero-curvature fixed point to study the $H_0$ tension. In this scheme, the equations restrict the universe’s evolution to certain scenarios, including radiation-like expansion, matter-like expansion, and late-time acceleration. Furthermore, we build the cosmographic series of the Fab-Four theory to obtain the kinematic parameters as the Hubble constant $H_0$ and the deceleration parameter $q_0$ for all the scenarios mentioned. Finally, we compare our results to find that it is possible to alleviate the current discrepancy on $H_0$ by considering specific requirements on the free parameters of the Fab-Four theory through a self-tuning filter.