Cosmic Growth in $f(T)$ Teleparallel Gravity

TL;DR

This paper investigates the growth index in various $f(T)$ teleparallel gravity models, analyzing structure formation without assuming the subhorizon limit, and providing numerical results for growth factors and indices.

Contribution

It introduces a generalized approach to study the growth factor in $f(T)$ models without immediate subhorizon approximation, allowing for more accurate analysis of structure formation.

Findings

Numerical growth factor and index results for multiple $f(T)$ models.

Identification of $k$ modes where subhorizon limit applies.

Enhanced understanding of structure formation in teleparallel gravity.

Abstract

Physical evolution of cosmological models can be tested by using expansion data, while growth history of these models is capable of testing dynamics of the inhomogeneous parts of energy density. The growth factor, as well as its growth index, gives a clear indication of the performance of cosmological models in the regime of structure formation of early Universe. In this work, we explore the growth index in several leading $f(T)$ cosmological models, based on a specific class of teleparallel gravity theories. These have become prominent in the literature and lead to other formulations of teleparallel gravity. Here we adopt a generalized approach by obtaining the M\'{e}sz\'{a}ros equation without immediately imposing the subhorizon limit, because this assumption could lead to over-simplification. This approach gives avenue to study at which $k$ modes the subhorizon limit starts to apply. We obtain numerical results for the growth factor and growth index for a variety of data set combinations for each $f(T)$ model.