Holographic Dark Energy with Torsion

TL;DR

This paper investigates holographic dark energy within Einstein-Cartan gravity incorporating axial torsion, ensuring the cosmological principle and geodesic consistency. By deriving the torsion-modified Friedmann equations and defining an effective density framework $\bar{\rho}$, $\bar{p}$ (with torsion contributions $\rho_{T}$, $p_{T}$), it analyzes holographic dark energy under three IR cut-offs: the Hubble radius, particle horizon, and future event horizon. The results show that the particle horizon fails to produce acceleration, while the future event horizon preserves acceleration; notably, the Hubble radius can yield acceleration in the superluminal torsion regime, and with $\gamma^{0} \approx 0.5$ one finds $\omega_{\Lambda} \approx -1$ today. These findings imply that torsion can broaden the viable implementations of holographic dark energy and potentially alleviate causality concerns associated with certain IR cut-offs, motivating further observational constraints on the torsion parameter. All key relations are expressed with the appropriate $P$-dot formalism and holographic scaling, revealing how axial torsion interplays with holographic bounds to shape the dark-energy equation of state $\omega_{\Lambda}$.

Abstract

We consider the holographic dark energy model with axial torsion which satisfy the cosmological principle. Subsequently, by using the torsional analogues of Friedmann equations for the new equation from Einstein-Cartan gravity theory, we obtain the equation of state for dark energy in this model. We find that the extended holographic dark energy from the particle horizon as the infrared (IR) cut-off does not give the accelerating expansion of the universe. Also, employing the future event horizon as IR cut-off still achieves the accelerating expansion of the universe. In contrast, there is a possibility that the Hubble radius as IR cut-off achieves to the accelerating expansion of the universe in superluminal region for axial torsion. More precisely, the current value of ratio for torsion to the matter density, $γ^{0}=0.5$ gives the equation of state of dark energy $ω_Λ\cong-1$.