Dark Energy Models in Relativistic Cosmology Framewor

Abstract

Late-time accelerated universe expansion is one of the most significant problems of the contemporary theoretical physics. In this paper, we have presented a detailed mathematical review of the dark energy models in the relativistic cosmology. Starting with the Einstein Field Equations and FriedmannLemaitreRobertsonWalker (FLRW) metric, we have obtained the basic kinematic conditions of cosmic acceleration. Although the conventional model of the standard percent  CDM has great phenomenological consistency with observational data, its physical interpretation suffers seriously due to theoretical obstacles namely the cosmological constant problem and the cosmic coincidence problem. This review therefore critically assesses other mathematical structures. Models of dynamical dark energy that are time-varying scalar field models such as quintessence and phantom energy, and the generalized Chaplygin Gas fluid mechanics are all analyzed. Moreover, we discuss geometric adjustments to General Relativity, namely, f(R) gravity, which mathematically resemble the dark energy without the need to introduce exotic macroscopic fluids. Lastly, we address the importance of observational constraints (Type Ia Supernovae, Baryon Acoustic Oscillations, and the Cosmic Microwave Background) to the above theoretical models, with a focus on the implication of the current tension in Hubble. As a result of this synthesis lies the need to have accuracy kinematic measurements of the next generation cosmological surveys in order to conclusively determine that a static vacuum energy nor a dynamically evolving gravitational sector.