Cosmographic reconstruction of $f(\mathcal{T})$ cosmology

TL;DR

This paper performs a model-independent cosmographic analysis to constrain the functional form of $f( ext{T})$ gravity models using observational data, revealing small deviations from the standard $ ext{Lambda}$CDM cosmology.

Contribution

It introduces a novel, model-independent method to reconstruct $f( ext{T})$ functions from cosmographic parameters, avoiding assumptions about specific models.

Findings

Constraints on $f( ext{T})$ compatible with observations

Small deviations from a constant $f( ext{T})$ suggest possible evolution of dark energy

Reconstruction aligns with theoretical predictions and cosmological principle

Abstract

A cosmographic reconstruction of $f(\mathcal T)$ models is here revised in a model independent way by fixing observational bounds on the most relevant terms of the $f(\mathcal T)$ Taylor expansion. We relate the $f(\mathcal T)$ models and their derivatives to the cosmographic parameters and then adopt a Monte Carlo analysis. The experimental bounds are thus independent of the choice of a particular $f(\mathcal T)$ model. The advantage of such an analysis lies on constraining the dynamics of the universe by reconstructing the form of $f(\mathcal T)$, without any further assumptions apart from the validity of the cosmological principle and the analyticity of the $f(\mathcal T)$ function. The main result is to fix model independent cosmographic constraints on the functional form of $f(\mathcal T)$ which are compatible with the theoretical predictions. Furthermore, we infer a phenomenological expression for $f(\mathcal T)$, compatible with the current cosmographic bounds and show that small deviations are expected from a constant $f(\mathcal T)$ term, indicating that the equation of state of dark energy could slightly evolve from the one of the $\Lambda$CDM model.