  We consider a generic cosmological model which allows for non-gravitational
direct couplings between dark matter and dark energy. The distinguishing
cosmological features of these couplings can be probed by current cosmological
observations, thus enabling us to place constraints on this generic interaction
which is composed of the conformal and disformal coupling functions. We perform
a global analysis in order to independently constrain the conformal, disformal,
and mixed interactions between dark matter and dark energy by combining current
data from: Planck observations of the cosmic microwave background radiation
anisotropies, a combination of measurements of baryon acoustic oscillations, a
supernovae Type Ia sample, a compilation of Hubble parameter measurements
estimated from the cosmic chronometers approach, direct measurements of the
expansion rate of the Universe today, and a compilation of growth of structure
measurements. We find that in these coupled dark energy models, the influence
of the local value of the Hubble constant does not significantly alter the
inferred constraints when we consider joint analyses that include all
cosmological probes. Moreover, the parameter constraints are remarkably
improved with the inclusion of the growth of structure data set measurements.
We find no compelling evidence for an interaction within the dark sector of the
Universe.
