We determine the range of parameter space of Interacting Quintessence Models
that best fits the recent WMAP measurements of Cosmic Microwave Background
temperature anisotropies. We only consider cosmological models with zero
spatial curvature. We show that if the quintessence scalar field decays into
cold dark matter at a rate that brings the ratio of matter to dark energy
constant at late times,the cosmological parameters required to fit the CMB data
are: \Omega_x = 0.43 \pm 0.12, baryon fraction \Omega_b = 0.08 \pm 0.01, slope
of the matter power spectrum at large scals n_s = 0.98 \pm 0.02 and Hubble
constant H_0 = 56 \pm 4 km/s/Mpc. The data prefers a dark energy component with
a dimensionless decay parameter c^2 =0.005 and non-interacting models are
consistent with the data only at the 99% confidence level. Using the Bayesian
Information Criteria we show that this exra parameter fits the data better than
models with no interaction. The quintessence equation of state parameter is
less constrained; i.e., the data set an upper limit w_x \leq -0.86 at the same
level of significance. When the WMAP anisotropy data are combined with
supernovae data, the density parameter of dark energy increases to \Omega_x
\simeq 0.68 while c^2 augments to 6.3 \times 10^{-3}. Models with quintessence
decaying into dark matter provide a clean explanation for the coincidence
problem and are a viable cosmological model, compatible with observations of
the CMB, with testable predictions. Accurate measurements of baryon fraction
and/or of matter density independent of the CMB data, would support/disprove
these models.Comment: 16 pages, Revtex4, 5 eps figures, to appear in Physical Review