Observational constraints of the modified cosmology through Barrow entropy

Understand

Taking into account a fractal structure for the black hole horizon, Barrow argued that the area law of entropy is modified due to quantum-gravitational effects (Barrow in Phys Lett B 808:135643, https://doi.org/10.1016/j.physletb.2020.135643, 2020).

• Accordingly, the corrected entropy takes the form $S \sim A^{1+\mathrm{\Delta}/2}$, where $0\leq\mathrm{\Delta}\leq1$, indicates the amount of the quantum-gravitational deformation effects.
• In this paper, based on Barrow entropy, we first derive the modified gravitational field equations through the Clausius relation.
• We then consider the Friedmann-Lema\^itre-Robertson-Walker (FLRW) metric as the background metric and derive the modified Friedmann equations inspired by Barrow entropy.