  A model of magnetic universe based on nonlinear electrodynamics has been
introduced by Kruglov. This model describes an early inflation era followed by
a radiation era. We show that this model is related to our model of universe
based on a quadratic equation of state. We discuss two quantitatively different
models of early universe. In Model I, the primordial density of the universe is
identified with the Planck density. At $t=0$, the universe had the
characteristics of a Planck black hole. During the inflation, which takes place
on a Planck timescale, the size of the universe evolves from the Planck length
to a size comparable to the Compton wavelength of the neutrino. If we interpret
the radius of the universe at the end of the inflation (neutrino's Compton
wavelength) as a minimum length related to quantum gravity and use Zeldovich's
first formula of the vacuum energy, we obtain the correct value of the
cosmological constant. In Model II, the primordial density of the universe is
identified with the electron density as a consequence of nonlinear
electrodynamics. At $t=0$, the universe had the characteristics of an electron.
During the inflation, which takes place on a gravitoelectronic timescale, the
size of the universe evolves from the electron's classical radius to a size
comparable to the size of a dark energy star of the stellar mass. If we
interpret the radius of the universe at the begining of the inflation
(electron's classical radius) as a minimum length related to quantum gravity
and use Zeldovich's second formula of the vacuum energy, we obtain the correct
value of the cosmological constant. This provides an accurate form of Eddington
relation between the cosmological constant and the mass of the electron. We
also introduce a nonlinear electromagnetic Lagrangian that describes
simultaneously the early inflation, the radiation era, and the dark energy era.
