Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1995-10-31
Class.Quant.Grav. 12 (1995) 3085-3102
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Latex, 29 pages, accepted for publication in Classical and Quantum Gravity
Scientific paper
10.1088/0264-9381/12/12/023
We use Boulware's Hamiltonian formalism of quadratic gravity theories in order to analyze the classical behaviour of Bianchi cosmological models for a Lagrangian density containing quadratic terms in the curvature. For this purpose we define a canonical transformation which leads to a clear distinction between two main variants of the quadratic theory, namely the R-squared or conformal Lagrangian densities. In this paper we restrict the study to the first variant. For Bianchi type I and IX models we give the explicit forms of the super-Hamiltonian constraint, of the ADM Hamiltonian density and of the corresponding canonical equations. In the case of a pure R-squared theory we solve these equations analytically for Bianchi I model. For Bianchi type IX model, we reduce the first-order equations of the Hamiltonian system to three coupled second-order equations for the true physical degrees of freedom. This discussion is extended to isotropic FLRW models.
Demaret Jacques
Querella Laurent
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