  We apply a parametric reconstruction method to a homogeneous, isotropic and
spatially flat Friedmann-Robertson-Walker (FRW) cosmological model filled of a
fluid of dark energy (DE) with constant equation of state parameter interacting
with dark matter (DM). The reconstruction method is based on expansions of the
general interaction term and the relevant cosmological variables in terms of
Chebyshev polynomials which form a complete set orthonormal functions. This
interaction term describes an exchange of energy flow between the DE and DM
within dark sector. To show how the method works we do the reconstruction of
the interaction function expanding it in terms of only the first three
Chebyshev polynomials and obtain the best estimation for the coefficients of
the expansion as well as for the DE equation of the state constant parameter w
using the type Ia Supernova SCP Union data set (307 SNe-Ia). The preliminary
reconstruction shows that in the best scenario there is an energy transfer from
DM to DE which worsen the problem of the cosmic coincidence in comparison with
the LCDM model. We conclude that this fact is an indication of a serious
drawback for the existence of such interaction between dark components.

General Relativity and Quantum Cosmology