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

The inclusion of a $\mathrm{\Lambda }$ term, today, in the relativistic field equations is consequence of the evolution of an observational cosmology. In this work we argue the “ansatz” $\mathrm{\Lambda }=\beta H^2+\frac{\alpha }{R^2}$ 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.