  This research aims to develop a new approach toward 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. We find
the value of the tiny coupling constant of gravity with electromagnetic fields,
which depends on the speed of light and 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, i.e., the
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.
