f(T) gravity mimicking dynamical dark energy. Background and perturbation analysis

TL;DR

This paper explores f(T) gravity models that replicate dynamical dark energy at the background level but differ in their perturbation growth, providing a method to reconstruct such models and analyze their observational distinctions.

Contribution

It introduces a formalism to reconstruct f(T) models for any dynamical dark energy scenario and analyzes their perturbation differences from standard models.

Findings

Perturbations distinguish f(T) models from each other despite identical background evolution.

Reconstructed f(T) models for quintessence show significant deviations in matter overdensity at small scales.

Deviations are negligible at large redshifts and large scales.

Abstract

We investigate f(T) cosmology in both the background, as well as in the perturbation level, and we present the general formalism for reconstructing the equivalent one-parameter family of f(T) models for any given dynamical dark energy scenario. Despite the completely indistinguishable background behavior, the perturbations break this degeneracy and the growth histories of all these models differ from one another. As an application we reconstruct the f(T) equivalent for quintessence, and we show that the deviation of the matter overdensity evolution is strong for small scales and weak for large scales, while it is negligible for large redshifts.