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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 $Λ=2π^2/λ^2$ that varies very slowly, being $λ=(c/H_0) R_H$ the graviton Compton wavelength. In the present work we use that the dark energy density parameter is given by $Ω_Λ=2π^2/3/R_H^2$, it only has the curvature $Ω_k$ as a free constant and depends exclusively on the radiation density parameter $Ω_r$. Using $Ω_{0r} = 9.54\times10^{- 5}$, the theoretical prediction for a flat universe of the dark energy density parameter is $Ω_{0Λ} = 0.6922$. 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 $Ω_{0k}=-0.003$. We conclude that the CMaDE model provides a natural explanation for the accelerated expansion and the coincidence problem of the universe.