  The Quintessence model is one of the simplest and better known alternatives
to Einstein's theory for gravity. The properties of the solutions have been
studied in great detail in the background, linear and non-linear contexts in
cosmology. Here we discuss new phenomenology that is induced by adding
disformal terms to the interactions. Among other results, we show analytically
and using cosmological simulations ran with the code \texttt{Isis} that the
model posses a mechanism through which is it possible to obtain repulsive fifth
forces, which are opposite to gravity. Although the equations are very complex,
we also find that most of the new phenomenology can be explained by studying
background quantities. We used our simulation data to test approximate
relations that exist between the metric and scalar field perturbations as well
as between the fifth force and gravity. Excellent agreement was found between
exact and approximated solutions, which opens the way for running disformal
gravity cosmological simulations using simply a Newtonian solver. These results
could not only help us to find new ways of testing gravity, but also provide
new motivations for building alternative models.
