Hamiltonian Formulation of Palatini f(R) theories a la Brans-Dicke

Details Hamiltonian Formulation of Palatini f(R) theories a la Brans-Dicke Hamiltonian Formulation of Palatini f(R) theories a la Brans-Dicke

2011-01-18

arxiv.org/abs/1101.3403v1

Phys.Rev.D83:104036,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, no figures

Scientific paper

10.1103/PhysRevD.83.104036

We study the Hamiltonian formulation of f(R) theories of gravity both in metric and in Palatini formalism using their classical equivalence with Brans-Dicke theories with a non-trivial potential. The Palatini case, which corresponds to the w=-3/2 Brans-Dicke theory, requires special attention because of new constraints associated with the scalar field, which is non-dynamical. We derive, compare, and discuss the constraints and evolution equations for the ww=-3/2 and w\neq -3/2 cases. Based on the properties of the constraint and evolution equations, we find that, contrary to certain claims in the literature, the Cauchy problem for the w=-3/2 case is well-formulated and there is no reason to believe that it is not well-posed in general.

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