Cosmography in f(T)-gravity

TL;DR

This paper uses cosmography to constrain f(T)-gravity models by deriving analytical relations between model derivatives and cosmographic parameters, enabling viability checks without solving complex equations.

Contribution

It provides analytical expressions linking f(T)-gravity derivatives to cosmographic parameters and applies these to constrain model viability.

Findings

Derived relations between f(T)-derivatives and cosmographic parameters.

Constrained f(T)-derivatives up to fifth order using cosmography.

Provided a model-independent way to test f(T)-gravity viability.

Abstract

Being based on the only assumption that the universe is homogenous and isotropic on large scales, cosmography is an ideal tool to investigate the cosmic expansion history in a almost model-independent way. Fitting the data on the luminosity distance and Baryon Acoustic Oscillations allows to determine the confidence ranges for the cosmographic parameters hence giving some quantitative constraints that a whatever theory has to fulfill. As an application, we consider here the case of teleparallel gravity (TEGR) also referred to as f(T)-gravity. To this end, we first work out analytical expressions to express the present day values of f(T)-derivatives as a function of the cosmographic parameters which hold under quite general and physically motivated conditions. We then use the constraints coming from cosmography to find out the confidence ranges for f(T)-derivatives up to the fifth order and show how these can be used to check the viability of given TEGR models without the need to explicitly solve the second order dynamic equations.