Self-Consistent Homogeneous Isotropic Cosmological Models. I. Generalities

Self-consistent models of uniform universes are provided by coupling Einstein's equations to the one-particle Liouville equation. Correlations between the "particles" of the cosmic gas are thus neglected. As a consequence, an equation of state is not needed in the theory but is, rather, provided from these statistical considerations. It is shown that an expanding self-consistent uniform universe behaves asymptotically as the relativistic polytrope $p\sim {\mu }^{\frac{5}{3}}$, and finally, as an expanding Friedmann universe. Near the possible singularity $R=0\mathrm{}$ ($R=\mathrm{scale}\mathrm{factor}$), self-consistent models are hot models. Friedmann models are shown to be a particular case of self-consistent models.