Turnaround radius in Horndeski’s theory

The evaluation of the recent concept of turnaround radius could be helpful in discriminating between the various theories of gravity; after a recap of the scalar-tensor theories, with particular relevance to the Horndeski’s theory, the concept of mass is exploited in order to give an alternative definition to the turnaround radius. This recent definition has proven more useful than the standard one, mainly because it turned out to be gaugeinvariant. Despite its unshakable differences with the standard definition using radial time-like geodesics, the hope is that such differences, as underlined in simpler cases, are small compared to the cosmological quantities involved. Thus, one can compare these simpler (and gauge-independent) predictions of the turnaround radius for the various theories of gravity with future data, finally finding which one will fits better them.