Imprint of massive neutrinos on Persistent Homology of large-scale structure

Exploiting the Persistent Homology technique and its complementary representations, we examine the footprint of summed neutrino mass ($M_{\nu}$) in the various density fields simulated by the publicly available Quijote suite. The evolution of topological features by utilizing the super-level filtration on three-dimensional density fields at zero redshift, reveals a remarkable benchmark for constraining the cosmological parameters, particularly $M_{\nu}$ and $\sigma_8$. The abundance of independent closed surfaces (voids) compared to the connected components (clusters) and independent loops (filaments), is more sensitive to the presence of $M_{\nu}$ for $R=5$ Mpc $h^{-1}$ irrespective of whether using the total matter density field ($m$) or CDM+baryons field ($cb$). Reducing the degeneracy between $M_{\nu}$ and $\sigma_8$ is achieved via Persistent Homology for the $m$ field but not for the $cb$ field. The uncertainty of $M_{\nu}$ at $1\sigma$ confidence interval from the joint analysis of Persistent Homology vectorization for the $m$ and $cb$ fields smoothed by $R=5$ Mpc $h^{-1}$ at $z=0$ reaches $0.0152$ eV and $0.1242$ eV, respectively. Noticing the use of the 3-dimensional underlying density field at $z=0$, the mentioned uncertainties can be treated as the theoretical lower limits.