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

  title={Various Hamiltonian formulations of f (R) gravity and their canonical relationships},
  author={Nathalie Deruelle and Yuuiti Sendouda and Ahmed Youssef},
  journal={Physical Review D},
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… 
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