Canonical equivalence in anisotropic models for higher order theory of gravity

Abstract

Different canonical formalisms for higher order theories lead to different phase-space structures of the Hamiltonian. Canonical equivalence of these Hamiltonians at the classical level does not assure the same in the quantum domain, due to nonlinearity. It has been proved in the isotropic models, that the “Dirac constraint analysis” (after taking care of divergent terms) and “Modified Horowitz Formalism” lead to identical phase-space structure of the Hamiltonian for the gravitational action with curvature squared terms. Here, we extend the same in anisotropic space-time, viz, Bianchi-I, Bianchi-III and Kantowski–Sachs models too. This is a prologue toward canonical quantization.