New Cases of Universality Theorem for Gravitational Theories

The “Universality Theorem” for gravity shows that f® 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® and standard gravity without cosmological constant is reproduced if f is the identity function (i.e. f®=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® theory. In particular for the function f®=R the standard equivalence between GR and Holst Lagrangian is obtained.