  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.
