  In a previous work it was shown that by considering the quantum nature of the
gravitational field mediator, it is possible to introduce the momentum energy
of the graviton into the Einstein equations as an effective cosmological
constant. The Compton Mass Dark Energy (CMaDE) model proposes that this
momentum can be interpreted as dark energy, with a Compton wavelength given by
the size of the observable universe $R_H$, implying that the dark energy varies
depending on this size. The main result of this previous work is the existence
of an effective cosmological constant $\Lambda=2\pi^2/\lambda^2$ that varies
very slowly, being $\lambda=(c/H_0) R_H$ the graviton Compton wavelength. In
the present work we use that the dark energy density parameter is given by
$\Omega_\Lambda=2\pi^2/3/R_H^2$, it only has the curvature $\Omega_k$ as a free
constant and depends exclusively on the radiation density parameter $\Omega_r$.
Using $\Omega_{0r} = 9.54\times10^{- 5}$, the theoretical prediction for a flat
universe of the dark energy density parameter is $\Omega_{0\Lambda} = 0.6922$.
We perform a general study for a non-flat universe, using the Planck data and a
modified version of the CLASS code we find an excellent concordance with the
Cosmic Microwave Background and Mass Power Spectrum profiles, provided that the
Hubble parameter today is $H_0 = 72.6$ km/s/Mpc for an universe with curvature
$\Omega_{0k}=-0.003$. We conclude that the CMaDE model provides a natural
explanation for the accelerated expansion and the coincidence problem of the
universe.
