Lagrangian Reconstruction of Barrow Holographic Dark Energy in Interacting Tachyon Model

Abstract

We consider a correspondence between the tachyon dark energy model and Barrow holographic dark energy (BHDE). The latter is a modified scenario based on the application of the holographic principle with Barrow entropy instead of the usual Bekenstein–Hawking one. We reconstruct the dynamics of the tachyon scalar field T in a curved Friedmann–Robertson–Walker universe both in the presence and absence of interactions between dark energy and matter. As a result, we show that the tachyon field exhibits non-trivial dynamics. In a flat universe, T˙2 must always be vanishing, independently of the existence of interaction. This implies ωD=−1 for the equation-of-state parameter, which in turn can be used for modeling the cosmological constant behavior. On the other hand, for a non-flat universe and various values of the Barrow parameter, we find that T˙2 decreases monotonically for increasing cos(Rh/a) and cosh(Rh/a), where Rh and a are the future event horizon and the scale factor, respectively. Specifically, T˙2≥0 for a closed universe, while T˙2<0 for an open one, which is physically not allowed. We finally comment on the inflation mechanism and trans-Planckian censorship conjecture in BHDE and discuss observational consistency of our model.