| Abstract: |
The accelerated expansion of the universe suggests the existence of dark energy, a component with negative pressure constituting nearly 70% of the cosmic energy budget. While the cosmological constant Λ with equation of state w=-1 remains the simplest explanation, persistent theoretical challenges and increasingly precise observations motivate the study of dynamical dark energy models in which w(z) evolves with cosmic time. This review provides a comprehensive analysis of parametric and non-parametric methods of modeling w(z), theoretical frameworks including quintessence, phantom fields, k-essence, coupled dark sectors, and modified gravity theories, and the latest observational constraints from DESI, CMB, BAO, supernovae, and large-scale structure. Special attention is devoted to the phenomenon of phantom-divide crossing (w=-1), its theoretical challenges, and mechanisms that allow such behavior without pathological instabilities. The review concludes with prospects from upcoming cosmological surveys and the implications for fundamental physics. |
