The possibility to avoid the cosmic initial singularity as a consequence of nonlinear effects on the Maxwell eletromagnetic theory is discussed. For a flat FRW geometry we derive the general nonsingular solution supported by a magnetic field plus a cosmic fluid and a nonvanishing vacuum energy density.The nonsingular behavior of solutions with a time-dependent Λ(t)-term are also examined. As a general result, it is found that the functional dependence of Λ(t) can uniquely be determined only if the magnetic field remains constant.All these models are examples of bouncing universes which may exhibit an inflationary dynamics driven by the nonlinear corrections of the magnetic field.

The thermodynamics of cosmological matter creation has been extensively investigated in the literature. In the context of general relativity, the particle production in the cosmological models is due to mechanisms such as an imperfect fluid with bulk viscosity or the decaying vacuum. Another interesting proposal is matter creation in cosmologies with variation of fundamental constants. In this work, we study the nonlinearity of the electrodynamics as a source of matter creation in cosmological models with flat Friedmann–Robertson–Walker (FRW) line geometry. We write the energy conservation law arising from Einstein field equations with cosmological term Λ, solve the field equations, and study how particles are created as the magnetic field B changes with cosmic epoch. We obtain solutions for the adiabatic particle creation rate, the total number of particles, and the scale factor as a function of time in three cases: Λ = 0, Λ = constant and Λ ∝ H2 (cosmological term proportional to the Hubble parameter). We find the constraints imposed by the second law of thermodynamics upon the cosmological solutions.

In recent years, there has been some renewed interest in cosmological models in which the constants of nature vary with time. In one of these, one supposes a dependence on the redshift of the fine structure constant as suggested by some astronomical observations of quasars. This has led, among others, to the proposal that the speed of light varies with the cosmological time. A Varying Speed of Light (VSL) would be able to solve some long standing problems of the standard cosmological model, without the need for inflation. In this work we study two models in which (1) c varies according to a power law of the scale factor c(t) ∝ a-r and (2) c is proportional to the Hubble parameter c(t) ∝ Hu. We present solutions for these two types of VSL cosmologies. We find that for a flat (k = 0) Friedmann–Robertson–Walker (FRW) universe, the variation of c is coupled to a cosmological Λ-term and both singular and non-singular solutions are possible.

In this work we investigate matter creation in the context of two types of varying speed of light (VSL) cosmologies. We write the energy conservation law arising from Einstein equations for a Friedmann-Robertson-Walker (FRW) line element in a flat universe, solve the field equations and study how particles are created as c changes with cosmic epoch. We calculate the "adiabatic" particle creation rate, the total number of particle as a function of time and find the constrains imposed by the second law of thermodynamics upon the models.