This research aims to provide the geometrical foundation of the uncertainty principle within a new causal structure of spacetime so-called Symmetrical Special Relativity (SSR), where there emerges a Lorentz violation due to the presence of an invariant minimum speed [Formula: see text] related to the vacuum energy. SSR predicts that a dS scenario occurs only for a certain regime of speeds [Formula: see text], where [Formula: see text], which represents the negative gravitational potentials ([Formula: see text]) connected to the cosmological parameter [Formula: see text]. For [Formula: see text], Minkowski (pseudo-Euclidean) space is recovered for representing the flat space ([Formula: see text]), and for [Formula: see text] ([Formula: see text]), Anti-de Sitter (AdS) scenario prevails ([Formula: see text]). The fact that the current universe is flat as its average density of matter distribution ([Formula: see text] given for a slightly negative curvature [Formula: see text]) coincides with its vacuum energy density ([Formula: see text] given for a slightly positive curvature [Formula: see text]), i.e. the cosmic coincidence problem, is now addressed by SSR. SSR provides its energy–momentum tensor of perfect fluid, leading to the EOS of vacuum ([Formula: see text]). Einstein equation for vacuum given by such SSR approach allows us to obtain [Formula: see text] associated with a scalar curvature [Formula: see text], whereas the solution of Einstein equation only in the presence of a homogeneous distribution of matter [Formula: see text] for the whole universe presents a scalar curvature [Formula: see text], in such a way that the presence of the background field [Formula: see text] opposes the Riemannian curvature [Formula: see text], thus leading to a current effective curvature [Formula: see text] according to observations. This corrects the notion of gravity as being only of Riemannian origin as the flat space has connection with a background gravity. In view of the current dS scenario with a quasi-zero [Formula: see text] slightly larger than [Formula: see text], we will just obtain a Generalized Uncertainty Principle (GUP) given in the cases of weak gravity and anti-gravity.