N-body simulations, halo mass functions, and halo density profile in $f(T)$ gravity

TL;DR

This paper uses N-body simulations to explore structure formation in $f(T)$ gravity, revealing observable differences from $ ext{Lambda}$CDM in matter distribution, halo mass functions, and lensing signals, potentially allowing empirical distinction between models.

Contribution

First detailed N-body simulation study of structure formation in $f(T)$ gravity, demonstrating observable differences from $ ext{Lambda}$CDM in large-scale structure and halo properties.

Findings

Matter power spectrum differs from $ ext{Lambda}$CDM, mainly due to expansion and gravitational constant changes.

Halo counts and mass distributions show significant differences, detectable via cluster statistics.

Weak lensing signals around low density regions are mildly different, offering observational tests.

Abstract

We perform N-body simulations for $f(T)$ gravity using the ME-Gadget code, in order to investigate for the first time the structure formation process in detail. Focusing on the power-law model, and considering the model-parameter to be consistent within 1$\sigma$ with all other cosmological datasets (such as SNIa, BAO, CMB, CC), we show that there are clear observational differences between $\Lambda$CDM cosmology and $f(T)$ gravity, due to the modifications brought about the latter in the Hubble function evolution and the effective $Newton\prime s$ constant. We extract the matter density distribution, matter power spectrum, counts-in-cells, halo mass function and excess surface density (ESD) around low density positions (LDPs) at present time. Concerning the matter power spectrum we find a difference from $\Lambda$CDM scenario, which is attributed to about 2/3 to the different expansion and to about 1/3 to the effective gravitational constant. Additionally, we find a difference in the cells, which is significantly larger than the Poisson error, which may be distinguishable with weak-lensing reconstructed mass maps. Moreover, we show that there are different massive halos with mass $M>10^{14}M_{\odot}/h$, which may be distinguishable with statistical measurements of cluster number counting, and we find that the ESD around LDPs is mildly different. In conclusion, high-lighting possible smoking guns, we show that large scale structure can indeed lead us to distinguish General Relativity and $\Lambda$CDM cosmology from $f(T)$ gravity.