Barrow holographic dark energy

We formulate Barrow holographic dark energy, by applying the usual holographic principle at a cosmological framework, but using the Barrow entropy instead of the standard Bekenstein-Hawking one. The former is an extended black-hole entropy that arises due to quantum-gravitational effects which deform the black-hole surface by giving it an intricate, fractal form. We extract a simple differential equation for the evolution of the dark-energy density parameter, which possesses standard holographic dark energy as a limiting subcase, and we show that the scenario can describe the thermal history of the universe, with the sequence of matter and dark-energy eras. Additionally, the new Barrow exponent significantly affects the dark-energy equation of state, and according to its value it can lead it to lie in the quintessence regime, in the phantom regime, or experience the phantom-divide crossing during the evolution.