Barrow entropy corrections to Friedmann equations

Recently, Barrow argued that quantum-gravitational effects may introduce intricate, fractal features on the black hole horizon J. D. Barrow, , The area of a rough black hole, Phys. Lett. B 808, 135643 (2020). In this viewpoint, black hole entropy no longer obeys the area law and instead it can be given by SA^1+/2, where the exponent ranges 01, and indicates the amount of the quantum-gravitational deformation effects. Based on this, and using the deep connection between gravity and thermodynamics, we disclose the effects of Barrow entropy on the cosmological equations. For this purpose, we start from the first law of thermodynamics, dE=TdS+WdV, on the apparent horizon of the Friedmann-Robertson-Walker universe, and derive the corresponding modified Friedmann equations by assuming that the entropy associated with the apparent horizon has the form of Barrow entropy. We also examine the validity of the generalized second law of thermodynamics for the Universe enclosed by the apparent horizon. Finally, we employ the emergence scenario of gravity and extract the modified Friedmann equation in the presence of Barrow entropy which coincides with one obtained from the first law of thermodynamics. When =0, the results of standard cosmology are deduced.