Early dark energy induced by non-linear electrodynamics

In this work, we introduce a parametrization of early dark energy that mimics radiation at early times and governs the present acceleration of the Universe. We show that such parametrization models non-linear electrodynamics in the early Universe and investigate the cosmological viability of the model. In our scenario, the early dark energy is encoded in the non-linearity of the electromagnetic fields through a parameter $\beta$ that changes the Lagrangian of the system, and the parameters $\gamma_s$ and $\alpha$, that define the departure from the standard model constant equation of state. We use a Bayesian method and the modular software \textsc{CosmoSIS} to find the best values for the model's free parameters with precomputed likelihoods from Planck 2018, primordial nucleosynthesis data, inferred distances from different wide galaxy surveys and luminosity distances of SNIa from Pantheon and SH0ES, such that $\gamma_s =$ 0.468 $\pm$ 0.026 and $\alpha =$ -0.947 $\pm$ 0.032, as opposed to $\Lambda$CDM where $\gamma_s = \beta =$ 0 and there is no equivalence for the $\alpha$ parameter. Our results predict an earlier formation of the structure and a shorter age of the Universe compared with the canonical cosmological model. One of the main findings of our work is that this kind of dark energy alleviates the ongoing tensions in cosmology, the Hubble tension and the so-called $\sigma_8$ tension, which predicted values by our model are H$_o =$ 70.2 $\pm$ 0.9 km/s/Mpc and $\sigma_8 =$ 0.798 $\pm$ 0.007. The reported values lie between the inferred values inferred from early and late (local) Universe observations. Future observations will shed light on the nature of the dark energy, its impact on the structure formation, and its dynamics.