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Physical Review D 80 (2009) 084032
Various Hamiltonian formulations of f(R) gravity and their canonical relationships
N. Deruelle1, Y. Sendouda2, A. Youssef1
(2009-10)

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.
1:  APC - UMR 7164 - AstroParticule et Cosmologie
2:  Yukawa Institute for Theoretical Physics
APC - THEORIE
Physics/General Relativity and Quantum Cosmology

Physics/High Energy Physics - Theory
Modified theories of gravity – Canonical formalism – Lagrangians – and variational principles – Lagrangian and Hamiltonian approach
Fulltext link: 
http://fr.arXiv.org/abs/0906.4983