  In this paper, we investigate a scenario in which late time cosmic
acceleration might arise due to coupling between dark matter and baryonic
matter without resorting to dark energy or large scale modification of gravity
associated with extra degrees of freedom. The scenario can give rise to late
time acceleration in Jordan frame and no acceleration in Einstein frame -
\textit{generic modification of gravity} caused by disformal coupling. Using a
simple parametrization of the coupling function, in maximally disformal case,
we constrain the model parameters by using the age constraints due to globular
cluster data. We also obtain observational constraints on the parameters using
$H(z)+SNIa+BAO$ data sets. In this case, we distinguish between phantom and non
phantom acceleration and show that the model can give rise to phantom behavior
in a narrow region of parameter space.
