Deformed Special Relativity with an invariant minimum speed as an explanation of the cosmological constant

Abstract

This paper shows the need of the emergence of a universal minimum speed in the space-time by means of a more thorough investigation of Dirac's large number hypothesis (LNH). We will realize that there should be a minimum speed $V$ with the same status of the invariance of the speed of light $c$, however $V$ has gravitational origin. Hence, such a minimum speed forms a new kinematic basis in the space-time, thus leading to a new Deformed Special Relativity (DSR) for the quantum world so-called Symmetrical Special Relativity (SSR). Furthermore, we will show that such a new structure of space-time (SSR) reveals a connection between $V$ and a preferred reference frame $S_V$ of background field that leads to the cosmological constant $\Lambda$, which can be associated with a cosmological anti-gravity. We will also investigate the effect of the number of baryons $N$ (Eddington number) of the observable universe on the Hydrogen atom. Finally, we will show that SSR-metric plays the role of a de-Sitter (dS)-metric with a positive cosmological constant, which could assume a tiny value.