Hamiltonian formalism and constraint analysis of three-form matter models coupled with general relativity
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 field is naturally present in string theory and cosmological scenarios. In particular, the action that is 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 is imposed. Interesting and relevant results about the number of dynamical degrees of freedom of these models are obtained. In addition, an analogy with a weakly coupled scalar field is discussed. Finally, as a particular example of this generic framework, a homogeneous and isotropic cosmological case is presented.