Unimodular f(T) gravity

TL;DR

This paper explores the reconstruction of $f(T)$ gravity within the unimodular framework, revealing unique properties of the generalized Friedmann equations and providing methods for reconstructing $f(T)$ functions without relying on specific scale factors.

Contribution

It introduces a reconstruction approach for $f(T)$ gravity in the unimodular setting, highlighting properties of the Friedmann equations and the role of Lagrange multipliers.

Findings

Reconstruction of $f(T)$ functions can be performed generally or specifically based on the scale factor.

Unimodular $f(T)$ gravity exhibits properties where Lagrange multipliers may or may not depend on time.

The reconstructed actions are consistent with unimodular gravity for constant $mbda$.

Abstract

We reconstruct the geometrical $f(T)$ actions in the framework of unimodular $f(T)$ gravity. The unimodular $f(T)$ gravity yields stunning properties related to the generalized Friedmann equations. Indeed, it has been found that depending on the form of the Friedmann equations, the Lagrange multipliers may or not depend on the time parameter $\tau$. Moreover we find that the reconstruction of $f(T)$ functions can be easily performed in general, not depending on a given scale factor, or can determine a particular way, depending on a given scale factor, in the vacuum. It is noted that the reconstruction of a general action joins is consistent to the unimodular gravity for the constant $\Lambda$