  Recently, in [1] we developed 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 (EOS) 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. In this article, we reconstruct the interaction
function expanding it in terms of only the first four Chebyshev polynomials and
obtain the best estimation for the coefficients of the expansion assuming three
models: (a) a DE equation of the state parameter w=-1 (an interacting
cosmological Lambda), (b) a DE equation of the state parameter w = constant
with a dark matter density parameter fixed, (c) a DE equation of the state
parameter w = constant with a free constant dark matter density parameter to be
estimated. In all the cases, the preliminary reconstruction shows that in the
best scenario there exist the possibility of a crossing of the noninteracting
line Q=0 in the recent past within the 1-sigma and 2-sigma errors from positive
values at early times to negative values at late times. This means that, in
this reconstruction, there is an energy transfer from DE to DM at early times
and an energy transfer from DM to DE at late times. We conclude that this fact
is an indication of the possible existence of a crossing behavior in a general
interaction coupling between dark components. Finally, we conclude that in this
scenario, the observations put strong constraints on the strength of the
interaction so that its magnitude can not solve the coincidence problem or at
least alleviate significantly.
