This work presents a complete cyclic cosmological scenario based on nonlinear
magnetic field. It is constructed a model composed by five fluids namely
baryonic matter, dark matter, radiation, neutrinos and a cosmological magnetic
field. The first four fluids are treated in the standard way and the fifth
fluid, the magnetic field, is described by a nonlinear electrodynamics. The
free parameters are fitted by observational data (SNIa, CMB, extragalactic
magnetic fields, etc) and by simple theoretical considerations. As result
arises a cyclic cosmological model which preserves the main successes of
standard big bang model and solve some other problems like the initial
singularity, the present acceleration and the Big Rip.Comment: 13 pages and 6 figure