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This paper shows the need of the emergence of a universal minimum speed inthe space-time by means of a more thorough investigation of Dirac's largenumber 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 kinematicbasis 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) revealsa connection between $V$ and a preferred reference frame $S_V$ of backgroundfield that leads to the cosmological constant $\Lambda$, which can beassociated with a cosmological anti-gravity. We will also investigate theeffect of the number of baryons $N$ (Eddington number) of the observableuniverse on the Hydrogen atom. Finally, we will show that SSR-metric plays therole of a de-Sitter (dS)-metric with a positive cosmological constant, whichcould assume a tiny value.

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