New cases of the universality theorem for gravitational theories

L Fatibene (1, 2) , M Ferraris (1, 2) , M Francaviglia (1, 2, 3)

1 Department of Mathematics
2 INFN
3 LCS

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 β R inspired by the Barbero-Immirzi formulation of GR (which in the Euclidean sector includes also selfdual formulation). It will be proven that f (β 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.

Mots clés: Physical Sciences

L Fatibene, M Ferraris, M Francaviglia. New cases of the universality theorem for gravitational theories. Classical and Quantum Gravity, 2010, 27 (16), pp.165021. ⟨10.1088/0264-9381/27/16/165021⟩. ⟨hal-00616269⟩