Cosmological imprints in the filament with DisPerSE

In the regime of cosmology and large-scale structure formation, filaments are vital components of the cosmic web. This study employs statistical methods to examine the formation, evolution, and cosmological constraints of filaments identified by DisPerSe. We run large-sample of N-body simulations to study the filament length and its evolution. In general, the filament length distribution can be fitted by a power law with both the normalization and power index dependent on redshift and cosmological parameters. It is discovered that filament length distribution is influenced by various cosmological parameters, with $\sigma_8$ and $n_s$ exhibiting slightly stronger dependence than $\Omega_m$. We also uncover a three-stage filament formation process from $z \sim 3$ to $z \sim 1$: rapid formation of both long and short filaments from $z \sim 3$ to $z \sim 2$, persistence of long filaments from $z \sim 2$ to $z \sim 1$, followed by fragmentation and increased prevalence of shorter filaments below $z \sim 1$. Finally, we employ initial power spectrum fluctuations to elucidate the cosmological dependence on the filament length function. These insights enhance our understanding of filament evolution and their cosmological relevance and also highlight the potential cosmological applications in observations.