New Cases of Universality Theorem for Gravitational Theories

The “Universality Theorem” for gravity shows that f(R) theories (in their metric-affine formulation) in vacuum are dynamically equivalent to vacuum Einstein equations with suitable cosmological constants. This holds true for a generic (i.e. except sporadic degenerate cases) analytic function f(R) and standard gravity without cosmological constant is reproduced if f is the identity function (i.e. f(R) = R). The theorem is here extended introducing in dimension 4 a 1-parameter family of invariants R inspired by the Barbero-Immirzi formulation of GR (which in the Euclidean sector includes also selfdual formulation). It will be proven that f(R) theories so defined are dynamically equivalent to the corresponding metric– affine f(R) theory. In particular for the function f(R) = R the standard equivalence between GR and Holst Lagrangian is obtained.