  We consider modifications to the Friedmann equation motivated by recent
proposals along these lines pursuing an explanation to the observed late time
acceleration. Here we show those modifications can be framed within a theory
with self-interacting gravity, where the term self-interaction refers here to
the presence of functions of $\rho$ and $p$ in the right hand side of the
Einstein equations. We then discuss the construction of the duals of the
cosmologies generated within that framework. After that we investigate the
modifications required to generate generalized and modified Chaplygin
cosmologies and show that their duals belong to a larger family of cosmologies
we call extended Chaplygin cosmologies. Finally, by letting the parameters of
those models take values not earlier considered in the literature we show some
representatives of that family of cosmologies display sudden future
singularities, which indicates their behavior is rather different from
generalized or modified Chaplygin gas cosmologies. This reinforces the idea
that modifications of gravity can be responsible for unexpected evolutionary
features in the universe.
