Universe made of baryonic gravitating particles behaves as a \Lambda CDM Universe

Using an approximate solution to the $N$-body problem in general relativity, and the \emph{principle of local isotropy at any point}, we construct a cosmological model, with zero curvature, for a universe composed uniquely by collision-less gravitating point-particles. The result is not, as currently thought, a null pressure Friedman model, but one that reproduces quite well the dark phenomena. We assume that there exist three consecutive ages with this property, formed by free atoms, stars and galaxies, respectively. Certainly, we are using a highly idealized view of the very complicated process going from uncoupled atoms to galaxies, but it allows us to obtain that the energy density at each epoch is of the form $\rho(a)=\frac{3H_0^2}{8\pi G}\left(\frac{\Omega_{ba}(1+\alpha)}{a^3}+ f(a)\right)$, where $\alpha$ is a constant, that we identify with the dark matter, and $f(a)$ a function of the scale factor, which is zero at galaxy formation and \emph{practically constant at the present epoch}, constant that we identify with the cosmological constant. The parameters of our model are the baryonic density $\Omega_{ba}$ and the redshifts $z"_i, z'_i, z_i$, corresponding to the effective decoupling of atoms and radiation, the formation of stars and galaxies respectively. The model sets a relation between the galaxy formation epoch and the amount of dark matter and dark energy, e.g., galaxy formation at $z_i \approx 11$ produces $\Omega_{\Lambda}=0.683$; and the function $f(a)$ predicts the begining of the acceleration recently at redshift $z\approx 0.6$, just as the $\Lambda CDM$ model. So, the dark phenomena could be related to a revision of the dynamical description of a gas of collision-less gravitating particles.