This research aims to develop a new approach towards a consistent coupling of electromagnetic and gravitational fields, by using an electron that couples with a weak gravitational potential by means of its electromagnetic field. To accomplish this, we must first build a new model which provides the electromagnetic nature of both the mass and the energy of the electron, and which is implemented with the idea of γ-photon decay into an electron-positron pair. After this, we place the electron (or positron) in the presence of a weak gravitational potential given in the intergalactic medium, so that its electromagnetic field undergoes a very small perturbation, thus leading to a slight increase in the field's electromagnetic energy density. This perturbation takes place by means of a tiny coupling constant ξ because gravity is a very weak interaction compared with the electromagnetic one. Thus, we realize that ξ is a new dimensionless universal constant, which reminds us of the fine structure constant α; however, ξ is much smaller than α because ξ takes into account gravity, i.e. ξ ∝ √ G. We find ξ = V /c ∼ = 1.5302 × 10 −22 , where c is the speed of light and V ∝ √ G( ∼ = 4.5876 × 10 −14 m/s) is a universal minimum speed that represents the lowest limit of speed for any particle. Such a minimum speed, unattainable by particles, represents a preferred reference frame associated with a background field that breaks the Lorentz symmetry. The metric of the flat spacetime shall include the presence of a uniform vacuum energy density, which leads to a negative pressure at cosmological scales (cosmological anti-gravity). The tiny values of the cosmological constant and the vacuum energy density will be successfully obtained in agreement with the observational data.

We aim to investigate the theory of Lorentz violation with an invariant minimum speed called Symmetrical Special Relativity (SSR) from the viewpoint of its metric. Thus, we should explore the nature of SSR-metric in order to understand the origin of the conformal factor that appears in the metric by deforming Minkowski metric by means of an invariant minimum speed that breaks down Lorentz symmetry. So, we are able to realize that there is a similarity between SSR and a new space with variable negative curvature (−∞ < R < 0) connected to a set of infinite cosmological constants (0 < Λ < ∞), working like an extended de Sitter (dS) relativity, so that such extended dS-relativity has curvature and cosmological "constant" varying in time. We obtain a scenario that is more similar to dS-relativity given in the approximation of a slightly negative curvature for representing the current universe having a tiny cosmological constant. Finally, we show that the invariant minimum speed provides the foundation for understanding the kinematics origin of the extra dimension considered in dS-relativity in order to represent the dS-length.

No abstract

No abstract

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.