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

@article{Deruelle2009VariousHF,
  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},
  year={2009},
  volume={80},
  pages={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… 
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References

SHOWING 1-10 OF 29 REFERENCES
A canonical formalism of f(R)-type gravity in terms of Lie derivatives
We propose a canonical formalism of f(R)-type gravity using a set of phase variables which is partly different from that used in the formalism of Buchbinder and Lyakhovich (BL). The new coordinates
The cosmological constant as an eigenvalue of f(R)-gravity Hamiltonian constraint
In the framework of ADM formalism, it is possible to find out eigenvalues of the WDW equation with the meaning of vacuum states, i.e. cosmological constants, for f(R) theories of gravity, where f(R)
A canonical formalism for a higher-curvature gravity
Following the method of Buchbinder and Lyakhovich, we carry out a canonical formalism for a higher-curvature gravity theory in which the Lagrangian density is given in terms of a function of the
Canonical quantisation and local measure of R 2 gravity
This work gives a generalisation of the Ostrogradsky method of bringing the higher-derivative theory to Hamiltonian form suitable for use in gauge theories. The Hamiltonian formalism is established
Boundary Terms, Variational Principles and Higher Derivative Modified Gravity
We discuss the criteria that must be satisfied by a well-posed variational principle. We clarify the role of Gibbons-Hawking-York type boundary terms in the actions of higher derivative models of
Hamiltonian formulation of Bianchi cosmological models in quadratic theories of gravity
We use Boulware's Hamiltonian formalism of quadratic gravity theories in order to analyse the classical behaviour of Bianchi cosmological models for a Lagrangian density in four spacetime dimensions.
Stability and Hamiltonian formulation of higher derivative theories.
  • Schmidt
  • Physics
    Physical review. D, Particles and fields
  • 1994
TLDR
The presumptions which lead to instabilities in theories of order higher than second are analyzed and the method proposed by Simon to bring fourth order gravity to second order can be (if suitably generalized) applied to bring sixth order gravityto second order.
The Hamiltonian formulation of higher order dynamical systems
Using Dirac's approach to constrained dynamics, the Hamiltonian formulation of regular higher order Lagrangians is developed. The conventional description of such systems due to Ostrogradsky is
f(R) Theories Of Gravity
Modified gravity theories have received increased attention lately due to combined motivation coming from high-energy physics, cosmology, and astrophysics. Among numerous alternatives to Einstein's
Variational Principles and Cosmological Models in Higher-Order Gravity
This dissertation investigates three main topics, all of which dealing with alternative, higher-order gravity theories in four dimensions. Firstly, we study the variational and conformal structure of
...
...