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arXiv · 1003.1617

New Cases of Universality Theorem for Gravitational Theories

L. Fatibene·M. Ferraris·M. Francaviglia
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Abstract

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.

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L. Fatibene, M. Ferraris, M. Francaviglia. 2010-03-18. New Cases of Universality Theorem for Gravitational Theories. https://doi.org/10.1088/0264-9381%2F27%2F16%2F165021

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