Cosmological Models of the Universe

Cosmological models are mathematical frameworks designed to describe the evolution and large-scale behavior of the Universe, grounded in observational evidence and primarily based on general relativity. By extending or modifying the gravitational sector, these models lead to different field equations and distinct cosmological implications, playing a central role in modern cosmology and shaping our understanding of fundamental physical phenomena. Among them, inflationary models provide compelling solutions to key problems of standard Big Bang cosmology, such as the flatness and horizon problems, while also offering mechanisms for the generation of primordial density perturbations responsible for the formation of large-scale structure. Measurements of cosmic microwave background (CMB) anisotropies and polarization are of particular importance for probing early-Universe physics and testing these scenarios, as well as models involving matter creation and primordial metric fluctuations. At late times, observational evidence for large-scale structure and cosmic acceleration points to the existence of dark matter and a nonzero cosmological constant, motivating the ΛCDM model as the current standard cosmological paradigm. Beyond isotropic descriptions, anisotropic cosmological models and theories based on generalized geometric frameworks, such as Finsler geometry, have also been developed to explore possible extensions of the spacetime structure. This Special Issue provides an overview of these developments on standard cosmological models, inflationary cosmology, the ΛCDM model, anisotropic cosmologies and Finsler cosmology.