Reconstruction from scalar-tensor theory and the inhomogeneous equation of state in f(T) Gravity

TL;DR

This paper explores f(T) gravity, a torsion-based modification of general relativity, reconstructing cosmological solutions using scalar fields and inhomogeneous equations of state, highlighting the equivalence of different approaches in explaining cosmic evolution.

Contribution

It introduces a method to reconstruct f(T) gravity models from various Hubble parameters and inhomogeneous equations of state, emphasizing the role of auxiliary scalar fields in cosmological solutions.

Findings

Reconstructed f(T) Lagrangians for different Hubble parameters.

Demonstrated equivalence between scalar field and exotic term approaches.

Showed that variations in Hubble parameter can be interpreted as modifications of gravity.

Abstract

General relativity (GR) characterizes gravity as a geometric properly exhibited as curvature on spacetime. Teleprallelism describes gravity through torsional properties, and can reproduce GR at the level of equations. Similar to f(R) gravity, on taking a generalization, f(T) gravity can produce various modifications its gravitational mechanism. The resulting field equations are inherently distinct to f(R) gravity in that they are second order. In the present work, f(T) gravity is examined in the cosmological context with a number of solutions reconstructed by means of an auxiliary scalar field. To do this, various forms of the Hubble parameter are considered with an f(T) lagrangian emerging for each instance. In addition, the inhomogeneous equation of state (EoS) is investigated with a particular Hubble parameter model used to show how this can be used to reconstruct the f(T) lagrangian. Observationally, both the auxiliary scalar field or exotic terms in the FRW field equations give the same results, meaning that the variation in the Hubble parameter may be interpreted as the need to reformulate gravity in some way as is done in f(T) gravity.