Lagrangian reconstruction of Barrow holographic dark energy in interacting tachyon model

TL;DR

This paper explores the connection between tachyon dark energy models and Barrow holographic dark energy, reconstructing scalar field dynamics in curved universes and analyzing implications for cosmology and the inflationary paradigm.

Contribution

It provides a novel reconstruction of tachyon scalar field dynamics within Barrow holographic dark energy, considering curvature and interactions, and discusses cosmological implications.

Findings

In flat universe, tachyon field behaves like a cosmological constant with =-1.

In non-flat universes,  varies with the horizon and scale factor, showing different behaviors for open and closed geometries.

The model's consistency with inflation and the Trans-Planckian Censorship Conjecture is discussed.

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 a non-trivial dynamics. In a flat Universe, $\dot T^2$ must always be vanishing, independently of the existence of interaction. This implies $\omega_D=-1$ 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 Barrow parameter, we find that $\dot T^2$ decreases monotonically for increasing $\cos(R_h/a)$ and $\cosh(R_h/a)$, where $R_h$ and $a$ are the future event horizon and the scale factor, respectively. Specifically, $\dot T^2\ge0$ for a closed Universe, while $\dot T^2<0$ 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.