Combined Studies Approach to Rule Out Cosmological Models Which Are Based on Nonlinear Electrodynamics

We apply a combined study in order to investigate the dynamics of cosmological models incorporating nonlinear electrodynamics (NLED). The study is based on the simultaneous investigation of such fundamental aspects as stability and causality, complemented with a dynamical systems investigation of the involved models, as well as Bayesian inference for parameter estimation. We explore two specific NLED models: the power-law and the rational Lagrangian. We present the theoretical framework of NLED coupled with general relativity, followed by an analysis of the stability and causality of the various NLED Lagrangians. We then perform a detailed dynamical analysis to identify the ranges where these models are stable and causal. Our results show that the power-law Lagrangian model transitions through various cosmological phases, evolving from a Maxwell radiation-dominated state to a matter-dominated state. For the rational Lagrangian model, including the Maxwell term, stable and causal behavior is observed within specific parameter ranges, with critical points indicating the evolutionary pathways of the universe. To validate our theoretical findings, we perform Bayesian parameter estimation using a comprehensive set of observational data, including cosmic chronometers, baryon acoustic oscillation (BAO) measurements, and supernovae type Ia (SNeIa). The estimated parameters for both models align with the expected values for the current universe, particularly the matter density Ωm and the Hubble parameter h. However, the parameters of the models are not tightly constrained within the prior ranges. Our combined studies approach rules out the mentioned models as an appropriate description of the cosmos. Our results highlight the need for further refinement and exploration of NLED-based cosmological models to fully integrate them into the standard cosmological framework.