Seeable universe and its accelerated expansion: an observational test

From the equivalence principle, one gets the strength of the gravitational effect of a mass $M$ on the metric at position r from it. It is proportional to the dimensionless parameter $\beta^2 = 2GM/rc^2$, which normally is $<< 1$. Here $G$ is the gravitational constant, $M$ the mass of the gravitating body, $r$ the position of the metric from the gravitating body and $c$ the speed of light. The seeable universe is the sphere, with center at the observer, having a size such that it shall contain all light emitted within it. For this to occur one can impose that the gravitational effect on the velocity of light at $r$ is zero for the radial component, and non zero for the tangential one. Light is then trapped. The condition is given by the equality $R_g = 2GM/c^2$, where $R_g$ represents the radius of the {\it seeable} universe. It is the gravitational radius of the mass $M$. The result has been presented elsewhere as the condition for the universe to be treated as a black hole. According to present observations, for the case of our universe taken as flat ($k = 0$), and the equation of state as $p = - \rho c^2$, we prove here from the Einstein's cosmological equations that the universe is expanding in an accelerated way as $t^2$, a constant acceleration as has been observed. This implies that the gravitational radius of the universe (at the event horizon) expands as $t^2$. Taking $c$ as constant, observing the galaxies deep in space this means deep in time as $ct$, linear. Then, far away galaxies from the observer that we see today will disappear in time as they get out of the distance ct that is $< R_g$. The accelerated expanding vacuum will drag them out of sight. This may be a valid test for the present ideas in cosmology. Previous calculations are here halved by our results.