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

TL;DR

This paper analyzes the cosmological evolution of fractional holographic dark energy within $f(T)$ gravity using dynamical systems, identifying critical points that correspond to different cosmic epochs and late-time acceleration.

Contribution

It provides a systematic phase-space analysis of FHDE in $f(T)$ gravity, revealing stable late-time accelerated solutions and the natural progression through cosmic epochs.

Findings

Identified four critical points including radiation, matter, and dark energy-dominated phases.

Found stable attractors corresponding to accelerated expansion and de Sitter solutions.

Demonstrated $f(T)$ gravity's capability to reproduce standard cosmological evolution.

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.