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As the black hole entropy does not obey the area law on it. The area law,given by $S\sim A^\delta\text{or}A^R$, where $\delta$ and $R$ , for$0\leq\delta\leq 1$, $0<R\leq 1$, indicates the amount of quantum gravitationaldeformation effects. This shows that gravity and thermodynamics are closelyrelated. Based on this deep connection, we tried to discuss the effects ofSharma-Mittal entropy on the cosmological equations. We also investigatedwhether the apparent horizon-enclosed universe was consistence with thegeneralized second law of thermodynamics. Finally, using the gravity emergencescenario, we derived the modified Friedmann equation and, compared it with thatderived from the first law of thermodynamics in the presence of Sharma-Mittalentropy. It is observed that we can recover the results for standard cosmologywhen $R,\delta=1$.

Correction to the Friedmann equation with Sharma-Mittal entropy: A new perspective on cosmology