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

ABSTRACT 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 superlevel 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 cold dark matter + baryons field ($\mathrm{ \mathrm{cb}}$). Reducing the degeneracy between $M_{\nu }$ and $\sigma _8$ is achieved via Persistent Homology for the m field but not for the $\mathrm{cb}$ field. The uncertainty of $M_{\nu }$ at $1\sigma$ confidenc interval from the joint analysis of Persistent Homology vectorization for the m and $\mathrm{cb}$ fields smoothed by $R=5$ Mpc $h^{-1}$ at $z=0$ reaches 0.0152 and 0.1242 eV, respectively. Noticing the use of the three-dimensional underlying density field at $z=0$, the mentioned uncertainties can be treated as the theoretical lower limits.