On the electrodynamics of moving particles in a quasi flat spacetime with Lorentz violation and its cosmological implications

Abstract

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 [Formula: see text]-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 [Formula: see text] because gravity is a very weak interaction compared with the electromagnetic one. Thus, we realize that [Formula: see text] is a new dimensionless universal constant, which reminds us of the fine structure constant [Formula: see text]; however, [Formula: see text] is much smaller than [Formula: see text] because [Formula: see text] takes into account gravity, i.e. [Formula: see text]. We find [Formula: see text], where [Formula: see text] is the speed of light and [Formula: see text][Formula: see text]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.