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 (Mν) 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 Mν and σ8. The abundance of independent closed surfaces (voids) compared to the connected components (clusters) and independent loops (filaments), is more sensitive to the presence of Mν 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 Mν and σ8 is achieved via Persistent Homology for the m field but not for the cb field. The uncertainty of Mν at 1σ confidenc 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.