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

N. Deruelle 1 Y. Sendouda 2 A. Youssef 1
1 APC - THEORIE
APC - UMR 7164 - AstroParticule et Cosmologie
Abstract : 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.
Document type :
Journal articles
Physical Review D, American Physical Society, 2009, 80, pp.084032. <10.1103/PHYSREVD.80.084032>


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Submitted on : Wednesday, October 10, 2012 - 6:17:15 PM
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N. Deruelle, Y. Sendouda, A. Youssef. Various Hamiltonian formulations of f(R) gravity and their canonical relationships. Physical Review D, American Physical Society, 2009, 80, pp.084032. <10.1103/PHYSREVD.80.084032>. <hal-00740746>

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