Deformed special relativity with an invariant minimum speed as an explanation of the cosmological constant

• Published in: Pramāṇa Vol. 96; no. 1
• Main Author: Cruz, Cláudio Nassif
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01-03-2022; Springer Nature B.V
• Subjects: Antigravity; Astronomy; Astrophysics and Astroparticles; Cosmological constant; Hydrogen atoms; Light speed; Observations and Techniques; Physics; Physics and Astronomy; Relativity; Theory of relativity; vacuum energy; Cosmological constant; 03.30.+p; 11.30.Qc; invariant minimum speed; dS-metric
• ISSN: 0304-4289; 0973-7111
• DOI: 10.1007/s12043-022-02296-0

This paper shows the need for the emergence of a universal minimum speed in the space–time by thoroughly investigating Dirac’s large number hypothesis (LNH). We realise 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, leading to a new deformed special relativity (DSR) for the quantum world so-called symmetrical special relativity (SSR). Furthermore, we show that such a new structure of space–time (SSR) reveals a connection between
V
and a preferred reference frame
S
V
of the background field, leading to the cosmological constant
Λ
, which can be associated with a cosmological antigravity. We also investigate the effect of the number of baryons
N
(Eddington number) of the observable Universe on the hydrogen atom. Finally, we show that SSR-metric plays the role of a de-Sitter (dS) metric with a positive cosmological constant, which could assume a tiny value.