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

TL;DR

This study uses Persistent Homology to analyze large-scale structure simulations, revealing how neutrino mass influences topological features and improving constraints on neutrino mass and cosmological parameters.

Contribution

It introduces a novel application of Persistent Homology to large-scale structure data for constraining neutrino mass and reducing parameter degeneracies.

Findings

Persistent Homology detects neutrino mass effects in topological features.

The method constrains neutrino mass with uncertainties of 0.0152 eV (m field) and 0.1242 eV (cb field).

Topological analysis helps reduce degeneracy between $M_{\nu}$ and $\sigma_8$.

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 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.