Evolutionary Behavior of Fractional Holographic Dark Energy within $f(T)$ Teleparallel Gravity

TL;DR

The paper studies fractional holographic dark energy (FHDE) within $f(T)$ gravity using a dynamical-systems approach in a spatially flat FRW universe. By introducing dimensionless variables and constructing an autonomous system, the authors identify four critical points corresponding to radiation, matter, FHDE-dominated de Sitter, and torsion-dominated de Sitter phases; radiation and matter epochs appear as saddle points, while two late-time attractors yield accelerated expansion. The analysis, including the dependence on the fractional parameter $\alpha$, shows that FHDE with a Hubble cutoff coupled to $f(T)$ gravity can reproduce the standard cosmic sequence and provide viable late-time acceleration, with nonhyperbolic cases at $\alpha=2$ explored via phase-space trajectories. Overall, the work demonstrates that FHDE within $f(T)$ gravity offers a consistent dynamical framework capable of describing the Universe's past, present, and future evolution under a unified approach.

Abstract

We investigate the cosmological dynamics of FHDE within $f(T)$ gravity by employing the dynamical system approach in a spatially flat FRW background. By introducing appropriate dimensionless variables, the field equations are reformulated as a closed system, which allows a systematic phase-space analysis. The resulting system admits four critical points, including two saddle points corresponding to radiation and matter-dominated epochs, and two stable points associated with a DE-dominated phase and a de Sitter solution. The radiation- and matter-dominated critical points are found to possess a saddle character in phase space, ensuring their transient nature and enabling the cosmological evolution to naturally progress toward a stable late-time accelerated attractor. The stable critical points describe accelerated expansion with effective equations of state compatible with DE and de Sitter regimes. Overall, the analysis indicates that $f(T)$ gravity is capable of reproducing the standard cosmological sequence within a consistent dynamical framework.

Figures (1)

• Figure 1: Phase portrait diagrams for the autonomous dynamical system with $\alpha=1.5$