Phenomenological Reconstruction of $f(T)$ Teleparallel Gravity

TL;DR

This paper introduces a new method to reconstruct $f(T)$ teleparallel gravity models from observationally motivated parameterizations, enabling the development of viable modified gravity scenarios aligned with cosmological data.

Contribution

It presents a novel reconstruction technique for $f(T)$ gravity based on phenomenological parameterizations, providing a practical toolkit for cosmological model building.

Findings

One model mimics $ ext{Lambda}$CDM behavior with tiny modifications.

The dark energy sector can be explained by modified gravity without a cosmological constant.

The method links observational parameterizations directly to viable $f(T)$ models.

Abstract

We present a novel reconstruction method of $f(T)$ teleparallel gravity from phenomenological parameterizations of the deceleration parameter or other alternatives. This can be used as a toolkit to produce viable modified gravity scenarios directly related to cosmological observations. We test two parameterizations of the deceleration parameter considered in recent literatures in addition to one parametrization of the effective (total) equation of state (EoS) of the universe. We use the asymptotic behaviour of the matter density parameter as an extra constraint to identify the viable range of the model parameters. One of the tested models shows how tiny modification can produce viable cosmic scenarios quantitatively similar to $\Lambda$CDM but qualitatively different whereas the dark energy (DE) sector becomes dynamical and fully explained by modified gravity not by a cosmological constant.