Gravity formulated as a classical gauge theory is based on the Mach principle in terms of curvature scalar $R$ by A. Einstein. The original idea of Einstein limits the gravity to act as a curvature in spacetime. However, there exist other possible classical fields such as torsion and non-metricity. The aim of this project is to make a compatible comparison between three paradigms: Gravity as curvature via Einstein-Hilbert action, Teleparallel Gravity (TEGR) and Coincidence Gravity (CGR). In TEGR a flat spacetime is considered as well as an asymmetric connection metric. In CGR, gravity is constructed in an equally flat tortionless spacetime which is ascribed to non-metricity.
The strength and weakness of each formulation is tested in the framework of a homogeneous and isotropic cosmological background. Mainly, the equivalence between GR and TEGR is examined at the level of equation of motion.
Also, we study the interactions between dark energy, dark matter and radiation and the stability of these models is explored. The implications of the interaction were tested in both early and late epoch of the Universe. It has been found that mostly there is a similarity of description of the evolution of the Universe provided by GR and TEGR while CGR always showed different description.