Hamiltonian formalism and constraint analysis of three-form matter models coupled with general relativity

TL;DR

This paper performs a Hamiltonian and constraint analysis of three-form matter models coupled with general relativity, relevant for cosmology and string theory, revealing degrees of freedom and their analogy with scalar fields.

Contribution

It provides a generic Hamiltonian framework for three-form fields coupled to gravity without imposing specific symmetries or potentials.

Findings

Determines the number of dynamical degrees of freedom.

Establishes an analogy with weakly-coupled scalar fields.

Includes a cosmological homogeneous and isotropic example.

Abstract

A Hamiltonian analysis of models given by a three-form field with a generic potential coupled to general relativity in four dimensions is performed. This kind of fields are naturally present in string theory and cosmological scenarios. In particular, the action that will be considered has been extensively used during the last years to propose inflationary and dark energy models. Nevertheless, in order to keep the discussion as generic as possible, neither symmetries nor a specific form of the potential for the three-form field will be imposed. Interesting and relevant results about the number of dynamical degrees of freedom of these models are obtained. In addition, the analogy with a weakly-coupled scalar field is discussed. Finally, as a particular example of this generic framework, the homogeneous and isotropic cosmological case will be presented.