Abstract
General relativity (GR) characterizes gravity as a geometric properly exhibited as curvature on spacetime. Teleparallelism 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, the auxiliary scalar field and the 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 in f(T) gravity.
Highlights
Modified gravity is one of the two direct approaches for reproducing the late-time acceleration observed in the universe [1,2,3]
There are other consistency problems that must eventually be tackled in the general relativity (GR) approach to gravity [4,5]
The question becomes what reformulation of gravity should be adopted, or whether we should take an extension of GR as our starting position
Summary
Modified gravity is one of the two direct approaches for reproducing the late-time acceleration observed in the universe [1,2,3]. The goal of the present work is to produce known and new Lagrangian models within the f (T ) gravity context using several Hubble parameter models [16], using an auxiliary scalar field as a conduit to perform this reconstruction. Where dots denote derivatives with respect to cosmic time With these governing equations in hand, an auxiliary scalar field can be introduced to reconstruct the f (T ) Lagrangian. Model 1 First a two term Hubble parameter which takes different forms at early and late times is considered. Hi would drive inflation and Hl would take on the small cosmological constant for late times Putting this into the scalar field functions in the Lagrangian in Eqs. A wide variety of potential Lagrangian terms emerge from considering this collection of Hubble parameter ansatzes
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