A brief review of a modified relativity that explains cosmological constant

Abstract

The present review aims to show that a modified space–time with an invariant minimum speed provides a relation with Weyl geometry in the Newtonian approximation of weak-field. The deformed Special Relativity so-called Symmetrical Special Relativity (SSR) has an invariant minimum speed V, which is associated with a preferred reference frame SV for representing the vacuum energy, thus leading to the cosmological constant (Λ). The equation of state (EOS) of vacuum energy for Λ, i.e., ρΛ=ϵ=−p emerges naturally from such space–time, where p is the pressure and ρΛ=ϵ is the vacuum energy density. With the aim of establishing a relationship between V and Λ in the modified metric of the space–time, we should consider a dark spherical universe with Hubble radius RH, having a very low value of ϵ that governs the accelerated expansion of universe. In doing this, we aim to show that SSR-metric has an equivalence with a de-Sitter (dS)-metric (Λ>0). On the other hand, according to the Boomerang experiment that reveals a slightly accelerated expansion of the universe, SSR leads to a dS-metric with an approximation for Λ<<1 close to a flat space–time, which is in the ΛCDM scenario where the space is quasi-flat, so that Ωm+ΩΛ≈1. We have Ωcdm≈23% by representing dark cold matter, Ωm≈27% for matter and ΩΛ≈73% for the vacuum energy. Thus, the theory is adjusted for the redshift z=1. This corresponds to the time τ0 of transition between gravity and anti-gravity, leading to a slight acceleration of expansion related to a tiny value of Λ, i.e., we find Λ0=1.934×10−35 s−2. This result is in agreement with observations.