Various Hamiltonian formulations of f(R) gravity and their canonical relationships

Details Various Hamiltonian formulations of f(R) gravity and their canonical relationships Various Hamiltonian formulations of f(R) gravity and their canonical relationships

2009-06-26

arxiv.org/abs/0906.4983v1

Phys.Rev.D80:084032,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, REVTeX 4

Scientific paper

10.1103/PhysRevD.80.084032

Various Hamiltonian formulations of f(R) gravity can be found in the literature. Some authors follow the Ostrogradsky treatment of higher derivative theories and introduce as extra variables first order time derivatives of the metric (typically the extrinsic curvature). Some others take advantage of the conformal equivalence of f(R) theory with Einstein's gravity coupled to a scalar field and introduce as an extra variable the scalar curvature R itself, which includes second time derivatives of the metric. We show that, contrarily to some claims, these formulations are related by canonical transformations.

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