Modified cosmology through Renyi and logarithmic entropies

We consider two different entropic corrections to Bekenstein entropy, namely Renyi entropy and logarithmic-corrected entropy, and develop the entropic force, heat flow across the horizon and pressure. We also derive the expressions for Newton’s law of gravitation and verify with Bekenstein entropy by taking [Formula: see text] in the case of Renyi entropy and [Formula: see text] for logarithmic entropy. The modified Friedmann equations are also being developed by using Newton’s first law of thermodynamics in both cases. In the presence of these equations, we also analyze the validity of generalized second law of thermodynamics for both entropy corrections on the apparent horizon. It is found that this law remains valid throughout the region under certain assumptions for nonflat FRW universe.