Exploring Dynamic Dark Energy Models in f(T) Gravity: A Comparative Study of NHDE, THDE, and BHDE

In this work, we explore the cosmological implications of three dynamic dark energy models-New Holographic Dark Energy (NHDE), Tsallis Holographic Dark Energy (THDE), and Barrow Holographic Dark Energy (BHDE)-within the framework of f(T) gravity. These models are motivated by the holographic principle and provide alternatives to the standard Lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Lambda $$\end{document}CDM model. We adopt a flat, isotropic Friedmann-Robertson-Walker (FRW) universe and employ a specific forms of f(T) gravity. The evolution of key cosmological parameters, such as the isotropic pressure, equation of state (EoS) parameter, and energy conditions, is analyzed for each model. Using observational data from Type Ia supernovae (SNIa), Cosmic Microwave Background (CMB), Baryon Acoustic Oscillations (BAO), and Hubble parameter measurements, we constrain the free parameters of each model and evaluate their compatibility with observational data. The analysis reveals that NHDE, THDE, and BHDE models are viable alternatives to Lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Lambda $$\end{document}CDM, offering a more dynamic description of dark energy. Each model satisfies key energy conditions, providing a stable framework for explaining cosmic acceleration. The results show deviations from the constant behavior of Lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Lambda $$\end{document}CDM, indicating the potential for time-evolving dark energy in these models.