In this thesis, we explain how to obtain Friedmann equations first by using theory of general relativity and then by considering the BecksteinHawking entropy as the cosmic entropy and applying the first law of thermodynamics to the apparent horizon. Then with considering Renyi entropy as the entropy of the apparent horizon, and applying the Clausius relation, modified Friedmann equations has been obtained in the Renyi cosmology. Then, with dynamical system approach, it has been shown that the obtained additional terms, compared to the standard Friedmann equations, may describe the current accelerated universe. In the final chapter of this thesis, we explain how to obtain Friedmann equations in the presence of the torsion field using Einstein-Cartan theory. We have also studied the evolution of these equations using the dynamical system approach in both cases of weak and constant torsion field.