Exploring the Evolution of Nonlinear Electrodynamics in the Universe: A Dynamical Systems Approach

• Published in: arXiv.org
• Main Authors: García-Salcedo, Ricardo, Gómez-Vargas, Isidro, González, Tame, Martinez-Badenes, Vicent, Quiros, Israel
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 30.06.2024
• Subjects: Astronomical models; Bayesian analysis; Cosmological constant; Cosmology; Critical point; Dynamic systems theory; Dynamical systems; Electrodynamics; Evolution; Measuring instruments; Parameter estimation; Physics - Cosmology and Nongalactic Astrophysics; Physics - General Relativity and Quantum Cosmology; Power law; Relativity; Stability; Statistical inference; System theory; Universe
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2407.00686

This paper investigates the dynamics of cosmological models incorporating nonlinear electrodynamics (NLED), focusing on their stability and causality. We explore two specific NLED models: the Power-Law and Rational Lagrangians. We assess these models' viability in describing the universe's evolution using dynamical systems theory and Bayesian inference. We present the theoretical framework of NLED coupled with general relativity, followed by an analysis of the stability and causality through the squared sound speed of the NLED Lagrangians. We then conduct a detailed dynamical analysis to identify the universe's evolution with this matter content. Our results show that the Power-Law Lagrangian model transitions through various cosmological phases 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 Type Ia Supernovae (SNeIa). The estimated parameters for both models align with expected values for the current universe, particularly the matter density \(\Omega_m\) and the Hubble parameter \(h\). However, the parameters \(\alpha\) and \(b\) are not tightly constrained within the prior ranges. Our model comparison strongly favors the \(\Lambda\)CDM model over the NLED models for late-universe observations, as the NLED model does not exhibit a cosmological constant behavior. Our results highlight the need for further refinement and exploration of NLED-based cosmological models to fully integrate them into the standard cosmological framework.