A study of holographic dark energy models using configuration entropy

The holographic dark energy models provide an alternative description of the dark energy. These models are motivated by the possible application of holographic principle to the dark energy problem. We study the one parameter Li holographic dark energy and the two parameter Barrow holographic dark energy models using configuration entropy of the matter distribution in the Universe. The configuration entropy rate exhibits a distinct minimum at a specific scale factor that corresponds to the epoch, beyond which the dark energy takes a driving role in the accelerated expansion of the Universe. We find that the location of the minimum and magnitude of the entropy rate at the minimum are sensitive to the parameters of the models. We find the best fit relations between these quantities and the parameters of each model. We propose that these relations can be used to constrain the parameters of the holographic dark energy models from the future measurements of the configuration entropy at multiple redshifts. Further, the Barrow holographic dark energy model is based on Barrow entropy which modifies the standard Bekenstein-Hawking entropy, to capture the deformation of the black-hole surface due to quantum gravitational effects. We find that the location and amplitude of the minimum of the configuration entropy rate is strongly sensitive to the deformation exponent $\Delta$ in the Barrow model. Our study suggests that signatures of the quantum gravitational effects on the future event horizon may be detected from the study of the configuration entropy of the matter distribution on large-scales.