Deformed Special Relativity with a minimum speed as explanation of the tiny value of the cosmological constant based on the Boomerang experiment in the ${\Lambda}CDM$ scenario

Abstract

In this paper we will show that a new structure of space-time with a minimum speed reveals a connection with Weyl geometry in the approximation of weak-field Newtonian limit. Symmetrical Special Relativity (SSR) has a minimum speed $V$ that plays the role of a preferred reference frame $S_V$ of vacuum that leads to the cosmological constant $\Lambda$. In order to realize such a connection between $V$ and $\Lambda$ within a scenario of space-time metric, we will use a model of spherical universe with Hubble radius $R_H$ filled by a low vacuum energy density $\rho_{\Lambda}$ that governs the accelerated expansion of the universe. In doing this, we will show that SSR-metric plays the role of a de-Sitter (dS)-metric with a positive cosmological constant ($\Lambda>0$). On the other hand, according to the Boomerang experiment as it is shown that the three-dimensional space of the universe is Euclidean and with a slightly accelerated expansion, SSR leads to a dS-metric with an approximation for $\Lambda<<1$ close to a flat space-time, which is in the $\Lambda CDM$ scenario where the space is quasi-flat, so that $\Omega_{m}+\Omega_{\Lambda}\approx 1$. We have $\Omega{cdm}\approx 23\%$ by representing dark cold matter, $\Omega_m\approx 27\%$ for matter and $\Omega_{\Lambda}\approx 73\%$ for the vacuum energy. Thus, the theory is adjusted for redshift $z=1$, i.e., the time $\tau_0$ at which the universe goes over from a decelerating to an accelerating expansion by obtaining the numerical value $\Lambda_0=1.934\times 10^{-35}s^{-2}$, being in good agreement with measurements.