On the role of Barrow's fractal entropy in the loop quantum gravity Barbero-Immirzi parameter

It is claimed that, using the Boltzmann-Gibbs statistical mechanics together with the Bekenstein-Hawking area entropy law, it is possible to determine a value for the Barbero-Immirzi parameter, . In this letter, we have shown that if we use Barrow's entropy rather than Bekenstein-Hawking's area entropy law then the Barbero-Immirzi parameter will depend on the Δ parameter. As a consequence, the loop quantum gravity area element will also depend on the Δ parameter.