A new type of $f(\mathcal{T})$ gravity from Barrow entropy

TL;DR

This paper introduces a novel cosmological model combining Barrow entropy modifications with $f(\mathcal{T})$ gravity, deriving new Friedmann equations and analyzing universe evolution, which aligns with current observations.

Contribution

It develops a unified framework integrating Barrow entropy with $f(\mathcal{T})$ gravity, resulting in a new model with modified Friedmann equations and cosmological implications.

Findings

The model's parameters are consistent with observational data.

The universe's dynamic evolution aligns with current cosmological observations.

The new model offers a promising avenue for further theoretical and observational studies.

Abstract

In this work, two originally separate adjustments for the Friedmann equations are concurrently considered. Firstly, the fractal structure of the black hole horizon region is imposed by the Barrow entropy. The second adjustment is the $f(\mathcal{T})$ gravity, which is based on a teleparallel framework generalization of the Einstein-Hilbert action, where $\mathcal{T}$ is the scalar torsion. This can be considered as a Barrow entropy modification of the $f(\mathcal{T})$ gravity thus yielding a new model. Gravity thermodynamics hypothesis principles are used to integrate these two models under a unified framework. We derive the modified Friedmann equation and note the corrections obtained. To understand the implications of such dual modifications, an application is analyzed and a particular $f(\mathcal{T})$ toy model is chosen for the purpose. The equation of the state parameter of the resulting model, the dimensionless density parameters of matter and dark energy, and the deceleration parameter are explored to check the viability of the new model. A discussion of the dynamic evolution of the universe follows from these results. It is seen that the results comply with the observations. The newly developed model is promising and demands further study.