Linear growth in power law $f(T)$ gravity

TL;DR

This paper derives the growth index for linear matter fluctuations in a power law $f(T)$ gravity model, extending previous models and allowing for redshift variation, providing insights into cosmic structure growth.

Contribution

It presents the first calculation of the growth index for the power law $f(T)$ gravity model and generalizes it to include redshift dependence.

Findings

Asymptotic growth index $oxed{rac{6}{11-6b}}$ for the model

Extension of $ ext{growth index}$ analysis to variable $ ext{redshift}$

Comparison with $ ext{Lambda CDM}$ model growth index

Abstract

We provide for the first time the growth index of linear matter fluctuations of the power law $f(T) \propto (-T)^{b}$ gravity model. We find that the asymptotic form of this particular $f(T)$ model is $\gamma \approx \frac{6}{11-6b}$ which obviously extends that of the $\Lambda$CDM model, $\gamma_{\Lambda}\approx 6/11$. Finally, we generalize the growth index analysis of $f(T)$ gravity in the case where $\gamma$ is allowed to vary with redshift.