Configuration entropy in the $\Lambda$CDM and the dynamical dark energy models: Can we distinguish one from the other?

The evolution of the configuration entropy of the mass distribution in the Universe is known to be governed by the growth rate of density perturbations and the expansion rate of the Universe. We consider the $\Lambda$CDM model and a set of dynamical dark energy models with different parametrization of the equation of state and explore the evolution of the configuration entropy in these models. We find that the nature of evolution of the configuration entropy depends on the adopted parametrization which may allow us to discern them from each other. The configuration entropy initially decreases with time but nearly plateaus out at present in the $\Lambda$CDM model. The models where dark energy becomes less dominant at late times exhibit a larger decrease in the configuration entropy compared to the $\Lambda$CDM model after redshift $z \sim 1$. We find that the configuration entropy remains nearly unchanged in the models where dark energy becomes more dominant at late times. Our results suggest that the method presented here may be also used to constrain the initial value of the configuration entropy of the Universe.