Early Dark Energy: A Review of Theoretical Models and Updated Observational Constraints

Abstract The discrepancy between early- and late-time determinations of the Hubble constant, known as the Hubble tension, has motivated a variety of extensions to the standard cosmological model. Among the proposed solutions, Early Dark Energy (EDE) scenarios have received significant attention due to their ability to modify the sound horizon at recombination and potentially alleviate this tension. In this review, we present an overview of EDE models, focusing on their theoretical foundations and phenomenological features. We also provide a dataset-oriented synthesis of EDE constraints, discussing how the inferred viability of EDE depends on the interplay between CMB datasets, local $$H_0$$ priors, large-scale structure probes, and parameter-volume effects. Our goal is to provide a unified and pedagogical account of how the theoretical realization of the EDE component and the choice of observational dataset jointly determine the inferred values of $$H_0$$ , $$f_{EDE}$$ , $$z_c$$ and $$S_8$$ . We further discuss the main challenges faced by these models, including their impact on large-scale structure observables, theoretical consistency issues, and remaining tensions with late-time data. Finally, we highlight prospects for future observational tests aimed at clarifying their role in the Hubble tension.