Geometrical Diagnostics for Modified Gravitational Theory with the Different Formalisms

Geometrical diagnostic methods were often applied to distinguish the gravitational models. But it is scarce investigate differences between different formalisms of modified theories (e.g. metric formalism and Palatini formalism). In this paper, we discriminate theory with by using geometrical methods. For a considered gravity f(R) or GBD theory), can see that difference two remarkable according results. And relative ΛCDM model, there are more deviations in than those formalism, {r, s} diagnostic. Given (generalized Brans-Dicke theory) time-variable Newton constant (VG) theory, VG constant-G studied. It indicates variation Newton’s could induce notable effects on quantities r, s q) both formalism.