Canonical equivalence in anisotropic models for higher order theory of gravity

TL;DR

This paper demonstrates that for anisotropic higher-order gravity models, two different Hamiltonian formalisms yield identical phase-space structures, extending previous isotropic results to more complex cosmological models.

Contribution

It shows the equivalence of Dirac and Modified Horowitz formalisms in anisotropic models with curvature squared terms, broadening understanding of Hamiltonian structures in higher-order gravity.

Findings

Dirac and Modified Horowitz formalisms produce identical phase-space structures in anisotropic models.

The result extends isotropic model findings to Bianchi-I, Bianchi-III, and Kantowski-Sachs models.

Supports the consistency of Hamiltonian approaches in complex gravitational theories.

Abstract

We show that as in the case of isotropic models, the `Dirac Algorithm' and `Modified Horowitz' Formalism' lead to identical phase-space structure of the Hamiltonian for the gravitational action with curvature squared terms, in anisotropic space-time, viz, Bianchi-I, Bianchi-III and Kantowski-Sachs models too.