Modified Hamiltonian formalism for Regge Teitelboim Cosmology

TL;DR

This paper introduces a modified Hamiltonian formalism for Regge-Teitelboim cosmology that overcomes limitations of the Ostrogradski approach, providing a direct and correct Hamiltonian formulation for the model.

Contribution

It presents an alternative Hamiltonian formalism applicable to higher derivative theories, specifically applied to the RT cosmological model, avoiding additional variables.

Findings

Derived the Hamiltonian for the RT model's scale factor.

Demonstrated the formalism's effectiveness for singular Lagrangians.

Provided a consistent Hamiltonian approach for higher derivative cosmological theories.

Abstract

The Ostrogradski approach for the Hamiltonian formalism of higher derivative theory is not satisfactory because of the reason that the Lagrangian cannot be viewed as a function on the tangent bundle to coordinate manifold. In this article, we have used an alternative approach which leads directly to the Lagrangian which, being a function on the tangent manifold, gives correct equation of motion; no new coordinate variables need to be added. This approach can be directly used to the singular (in Ostrogradski sense) Lagrangian. We have used this method for the Regge Teitelboim (RT) minisuperspace cosmological model. We have obtained the Hamiltonian of the dynamical equation of the scale factor of RT model.