Chen-Wu type model and the total energy of the universe

The inclusion of a $\Lambda $ term, today, in the relativistic field equations is consequence of the evolution of an observational cosmology. In this work we argue the "ansatz" $\Lambda = \beta H^2 +\frac{\alpha}{R^2}$ is applicable to the total energy density of the universe, discuss some cosmological consequences and compare the growing mode of the density contrast with the corresponding mode of the standard model.