Two-component universe containing ordinary mater and a new component of the form $\frac{l}{R}\rho$

Abstract

We consider a model of the universe described by Einstein equations whose the right-hand side consists of ordinary energy-momentum tensor and an effective vacuum energy-momentum tensor with $\rho^{vac}=-p^{vac}=L_c/K$, where $L_c=8\pi Gl\rho R^{-1}$ and $\rho$ is the mass density of cosmical medium, $l$ the constat with dimension $[cm]$ and $R$ the scale factor of the expanding universe. We determine the vacuum energy density assigned to the term $L_c$ as a function of the scale factor and, when taking $l=2R_0$, $R_0$ being the present 'radius' of the universe, and $\Omega_0=0.3$, the normalized vacuum mass density, we obtain $\Omega_t=1$, deceleration parameter $q_0\approx -0.5$ and the age of the universe $t_0\approx 0.9\times H_0^{-1}$. The values are compatible with the estimated observatory values of cosmic parameters. Finally, we try to interpret the energy content of $L_c$ as the field energy of a field whose source is the ordinary matter in the universe.