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 classical possible fields such as torsion and non-metricity. The aim of this M.Sc thesis is to make a compatible comparison between three paradigms: Gravity as curvature via Einstein-Hilbert action, Teleparallel Gravity (TEGR) and Coincidence Gravity (CGR). 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. Models were established to describe the interactions between dark energy, dark matter and radiation. The stability of these models was explored. The implications of the interaction were tested in both early and late epoch of the Universe. It was found that mostly there is similar description of the evolution of the Universe provided by GR and TEGR while CGR always showed di↵erent description.