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In this paper we will show that a new structure of space-time with a minimumspeed reveals a connection with Weyl geometry in the approximation ofweak-field Newtonian limit. Symmetrical Special Relativity (SSR) has a minimumspeed $V$ that plays the role of a preferred reference frame $S_V$ of vacuumthat leads to the cosmological constant $\Lambda$. In order to realize such aconnection between $V$ and $\Lambda$ within a scenario of space-time metric, wewill use a model of spherical universe with Hubble radius $R_H$ filled by a lowvacuum energy density $\rho_{\Lambda}$ that governs the accelerated expansionof the universe. In doing this, we will show that SSR-metric plays the role ofa de-Sitter (dS)-metric with a positive cosmological constant ($\Lambda>0$). Onthe other hand, according to the Boomerang experiment as it is shown that thethree-dimensional space of the universe is Euclidean and with a slightlyaccelerated expansion, SSR leads to a dS-metric with an approximation for$\Lambda<<1$ close to a flat space-time, which is in the $\Lambda CDM$ scenariowhere 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 thevacuum 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 acceleratingexpansion by obtaining the numerical value $\Lambda_0=1.934\times10^{-35}s^{-2}$, being in good agreement with measurements.

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