We perform $N$-body simulations for $f(T)$ gravity using the ME-Gadget code, in order to investigate the structure formation process in detail for the first time. Focusing on the power-law model and considering the model parameter to be consistent within $1\sigma$ with all other cosmological data sets (such as type 1a supernovae, baryon acoustic oscillations, the cosmic microwave background, and cosmic chronometers), we show that there are clear observational differences between $\mathrm{\Lambda }\mathrm{CDM}$ cosmology and $f(T)$ gravity due to the modifications brought about by the latter in the evolution of the Hubble function and the effective Newton’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 the present time. Concerning the matter power spectrum, we find a difference from that in the $\mathrm{\Lambda }\mathrm{CDM}$ scenario, about $2/3$ of which is attributed to the different expansion and 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 masses $M>{10}^{14}{M}_{\odot }/h$, which may be distinguishable from statistical measurements of cluster number counting, and we find that the ESD around LDPs is mildly different. In conclusion, by highlighting possible smoking guns, we show that large-scale structure can indeed lead us to distinguish general relativity and $\mathrm{\Lambda }\mathrm{CDM}$ cosmology from $f(T)$ gravity.

中文翻译：

---

N 体模拟、晕质量函数和晕密度分布 inf(T)gravity

我们执行$ñ$- 身体模拟$F(吨)$重力使用ME-Gadget代码，首次详细研究结构形成过程。关注幂律模型，考虑模型参数在$1\sigma$与所有其他宇宙学数据集（如 1a 型超新星、重子声学振荡、宇宙微波背景和宇宙天文钟），我们表明两者之间存在明显的观测差异$\mathrm{\Lambda }\mathrm{清洁发展机制}$宇宙学和$F(吨)$由于后者在哈勃函数和有效牛顿常数的演化中带来的修改。我们提取了目前低密度位置 (LDPs) 周围的物质密度分布、物质功率谱、细胞计数、晕质量函数和超表面密度 (ESD)。关于物质功率谱，我们发现与$\mathrm{\Lambda }\mathrm{清洁发展机制}$情景，关于$2/3$其中归因于不同的膨胀和大约$1/3$为有效引力常数。此外，我们发现细胞的差异明显大于泊松误差，这可能与弱透镜重建的质量图区分开来。此外，我们表明存在不同质量的大质量晕$米>{10}^{14}{米}_{\odot }/H$，这可能与簇数计数的统计测量有区别，我们发现 LDP 周围的 ESD 略有不同。总之，通过突出可能的确凿证据，我们表明大尺度结构确实可以引导我们区分广义相对论和$\mathrm{\Lambda }\mathrm{清洁发展机制}$宇宙学$F(吨)$重力。