# Reconstructing $f(T)$ modified gravity from ECHDE and ECNADE models

## TL;DR

This paper reconstructs $f(T)$ gravity models from holographic and agegraphic dark energy theories, showing they can explain current cosmic acceleration, exhibit phantom or quintessence behaviors, and align with observational data.

## Contribution

It introduces a method to reconstruct $f(T)$ gravity from entropy-corrected holographic and agegraphic dark energy models, analyzing their stability and observational compatibility.

## Key findings

- Models exhibit phantom or quintessence behavior.
- Transition between quintessence and phantom phases observed.
- Physical parameters align with current observational data.

## Abstract

We investigate alternative candidates to dark energy that can explain the current state of the universe in the framework of the generalized teleparallel theory of gravity $f(T)$ where $T$ denotes the torsion scalar. To achieve this, we carried out a series of reconstruction taking into account to the ordinary and entropy-corrected versions of the holographic and new agegraphic dark energy models. These models used as alternative to dark energy in the literature in order describe the current state of our universe. It is remarked that the models reconstructed indicates behaviors like phantom or quintessence models. Furthermore, we also generated the EoS parameters associated to entropy-corrected models and we observed a transition phase between quintessence state and phantom state as showed by recent observational data. We also investigated on the stability theses models and we created the $\{r-s\}$. The behavior of certains physical parameters as speed of sound and the Statefinder parameters are compatible with current observational data.