  In this work, we propose an economical model to address some open
cosmological problems such as the absence of the initial cosmological
singularity, an early acceleration of the Universe and the generation of
matter-antimatter asymmetry. The model is based on a scenario in which the
early Universe consists of a non-linear electrodynamics fields. It is found
that the non-linear electrodynamics model has an equation of state
$p=\frac{1}{3} \rho - \frac{4}{3} \beta \rho^{1+\alpha}$ which shows that the
Universe undergoes an early epoch acceleration to a radiation era given by $p
=\frac{1}{3} \rho$. We show that the singularities in the energy density,
pressure and curvature are absent at early stages. In our scenario, the baryon
asymmetry is generated by the non-linearity parameter $\beta$. Additionally, we
calculate the resulting baryon asymmetry and discuss how a successful
gravitational baryogenesis is obtained for different values of the model's
parameter space.
