Holographic dark energy through Loop Quantum Gravity inspired entropy

We construct a new cosmological holographic dark energy scenario based on Loop Quantum Gravity inspired entropy, instead of the standard Bekenstein-Hawking one. The former is an extended black-hole entropy that arises from non-extensive statistics and quantum geometry and is quantified by a new dimensionless parameter $q$, which possesses standard holographic dark energy as a particular sub-case. In the future event horizon as the Infrared cutoff, we provide a simple differential equation for the dark energy density parameter, as well as an analytical expressions for the corresponding equation-of-state and deceleration parameters. We show that the scenario at hand can describe successfully the usual thermal history of the Universe, with the sequence of matter and dark-energy epochs, while the transition to acceleration takes place at $z\approx 0.6$. Additionally, according to the value of the new entropic parameter $q$, the dark energy equation-of-state parameter can have a rich behavior, and it can be quintessence-like, phantom-like, or experience the phantom-divide crossing.