Arbitrarily coupled $p-$forms in cosmological backgrounds
Abstract
In this paper we consider a model based on interacting forms and explore some cosmological applications. Restricting to gauge invariant actions, we build a general Lagrangian allowing for arbitrary interactions between the forms (including interactions with a form, scalar field) in a given background in dimensions. For simplicity, we restrict the construction to up to first order derivatives of the fields in the Lagrangian. We discuss with detail the four dimensional case and devote some attention to the mechanism of topological mass generation originated by couplings of the form between a form and a form. As a result, we show the system of the interacting forms is equivalent to a parity violating, massive, Proca vector field model. Finally, we discuss some cosmological applications. In a first case we study a very minimalistic system composed by a form coupled to a form. The form induces an effective potential which acts as a cosmological constant term suitable to drive the late time accelerated expansion of the universe dominated by dark energy. We study the dynamics of the system and determine its critical points and stability. Additionally, we study a system composed by a scalar field and a -form. This case is interesting because the presence of a coupled form can generate non vanishing anisotropic signatures during the late time accelerated expansion. We discuss the evolution of cosmological parameters such as the equation of state in this model.
Keywords
Cite
@article{arxiv.1810.05301,
title = {Arbitrarily coupled $p-$forms in cosmological backgrounds},
author = {Juan P. Beltrán Almeida and Alejandro Guarnizo and César A. Valenzuela-Toledo},
journal= {arXiv preprint arXiv:1810.05301},
year = {2020}
}
Comments
Several modifications and updates. The discussion about the $3-$forms is reviewed and corrected. A new application included. Several references added. Main conclusions unchanged