Note on agegraphic dark energy inspired by modified Barrow entropy

We revisit agegraphic dark energy (ADE) model when the entropy associated with the apparent horizon is in the form of Barrow entropy, $S\sim A^{1+\delta/2}$, where $0\leq\delta\leq1$ indicates the amount of the quantum-gravitational deformation effects of the horizon. The modification to the entropy expression, not only change the energy density of ADE, but also modifies the Friedmann equations due to thermodynamics-gravity conjecture. Based on this, we investigate the cosmological consequences of ADE through modified Barrow cosmology and disclose the effects of Barrow exponent $\delta$ on the evolutions of the cosmological parameters. We observe that, depending on the values of $\delta$, the transition from early decelerated phase to the late time accelerated phase occurs, and the equation of state (EoS) parameter $w_{de}$ varies from quintessence $-1<w_{de}<-1/3$ to the phantom regime $(w_{de}<-1)$. When $\delta=0$, all results of ADE in standard cosmology are restored.