  In this work, we investigate thick brane models with a single three-form
field. We find novel solutions for thick braneworlds where only three-forms
exist and interact gravitationally in the bulk, both with and without matter
fields. We use an additional scalar field as proxy for the matter fields. As an
initial study, we consider the results here in contrast to the single scalar
field thick braneworld case. The properties of the specific three-form
parameterisation limits the freedom we have to choose the form of the warp
factor, leading to a closed system of equations with nontrivial yet unstable
solutions. The stability of the gravitational sector for thick brane
three-forms is investigated and the models are shown to be unstable against
small perturbations of the metric, further indicating that three-forms cannot
exist stably in thick braneworld settings.
