Seeable universe and its accelerated expansion: an observational test

TL;DR

This paper proposes an observational test for the accelerated expansion of the universe based on the gravitational radius and the seeable universe concept, linking it to black hole conditions and Einstein's cosmological equations.

Contribution

It introduces a novel observational test for cosmic acceleration using the gravitational radius and seeable universe framework, connecting black hole conditions with cosmological expansion.

Findings

The universe's gravitational radius expands as t^2.

Deep space galaxies will eventually disappear as they move beyond the observable horizon.

The universe's accelerated expansion can be derived from Einstein's equations with specific conditions.

Abstract

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.