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

Abstract

Black hole entropy does not obey the area law. The area law, given by S∼Aδ or AR, where δ and R , for 0≤δ≤1, 0<R≤1, indicates the amount of quantum gravitational deformation effects. This shows that gravity and thermodynamics are closely related. The modification to the entropy expression, not only change the energy density of ADE, but also modifies the Friedmann equations due to the thermodynamics-gravity conjecture. Based on this deep connection, we discuss the effects of cosmological equations and consequences of agegraphic dark energy (ADE) through modified Sharma–Mittal entropy. We also investigate whether the apparent horizon-enclosed universe was consistent with the generalized second law of thermodynamics or not? Finally, using the gravity emergence scenario, we derive the modified Friedmann equation and compare it with that derived from the first law of thermodynamics in the presence of Sharma–Mittal entropy. We can recover the results for standard cosmology when R,δ=1.