Arbitrarily coupled $p-$forms in cosmological backgrounds

TL;DR

This paper develops a general framework for interacting $p$-forms in cosmology, revealing how they can generate effective cosmological constants, mass terms, and anisotropic signatures, with potential implications for dark energy and universe evolution.

Contribution

It introduces a gauge-invariant Lagrangian for arbitrary interacting $p$-forms in cosmological backgrounds, including mechanisms for topological mass generation and applications to dark energy models.

Findings

Interacting $p$-forms can produce effective cosmological constants.

Couplings induce parity-violating, massive vector fields.

Models can generate anisotropic signatures during late-time acceleration.

Abstract

In this paper we consider a model based on interacting $p-$forms and explore some cosmological applications. Restricting to gauge invariant actions, we build a general Lagrangian allowing for arbitrary interactions between the $p-$forms (including interactions with a $0-$form, scalar field) in a given background in $D$ 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 $B\wedge F$ between a $p-$form and a $(3-p)-$form. As a result, we show the system of the interacting $p-$forms $(p=1,2,3)$ 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 $3-$form coupled to a $0-$form. The $3-$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 $1$-form. This case is interesting because the presence of a coupled $1-$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.