  In this work we consider gravitational theories in which the effect of
coupling characteristic classes, appropriately introduced as operators in the
Einstein-Hilbert action, has been taken into account. As it is well known, this
approach strays from the framework of general relativity since it results in
theories in which torsion can be present. We consider here all the
characteristic classes that are consistent with a four-dimensional space-time
manifold. Then, we present explicit expressions for the contortion $1$-form and
torsion $2$-form that can be obtained under general conditions in various cases
of interest. Additionally, we use the same framework to study cosmological
scenarios that are obtained mainly by selecting the flat FLRW metric and an
ideal fluid.
