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

TL;DR

This work introduces a topological approach based on Persistent Homology (PH) to quantify the imprint of massive neutrinos on the nonlinear large-scale structure, using the Quijote N-body simulations. By vectorizing PH outputs (Betti numbers, and complementary quantities B_k and P_k) for both the total matter field $m$ and the CDM+baryons field $cb$, the study assesses how neutrino mass modulates topological features at $z=0$ under different smoothing scales. Fisher forecasts show that PH, especially when combining $m$ and $cb$ with multiple topological statistics, can tighten constraints on $M_\nu$ and partially break its degeneracy with $\sigma_8$, with projected 1σ uncertainties of about $1.5\times 10^{-2}$ eV (for $m$) and $\sim 0.12$ eV (for $cb$) at $R=5\,h^{-1}$ Mpc, $z=0$. The results underscore PH as a powerful, multi-scale, morphology-based probe complementary to standard two-point statistics, with important implications for leveraging upcoming surveys to constrain neutrino masses.

Abstract

Exploiting the Persistent Homology technique and its complementary representations, we examine the footprint of summed neutrino mass ($M_ν$) 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 $M_ν$ and $σ_8$. The abundance of independent closed surfaces (voids) compared to the connected components (clusters) and independent loops (filaments), is more sensitive to the presence of $M_ν$ 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 $M_ν$ and $σ_8$ is achieved via Persistent Homology for the $m$ field but not for the $cb$ field. The uncertainty of $M_ν$ at $1σ$ 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.

Figures (13)

• Figure 1: Evolution of topological features by changing the filtration parameter (known as proximity parameter) in the context of super-level filtration for a 2-dimensional mock density field. The left panel shows the density field and the number (color) assigned to each cell indicates the value of density contrast ($\delta$). The sub-complexes corresponding to the proximity level $\vartheta= \{5,4,2\}$ in such that $\delta (\boldsymbol{r})\ge \vartheta$ are indicated by assigning the dark color for pixels in the second, third, and fourth panels from the left to right, respectively.
• Figure 2: Excursion sets were made with super-level filtration on the density field for a fiducial realization from Quijote simulations. We cropped box of $156$ Mpc $h^{-1}$ size from the original volume. The density field is constructed based on the particle position at $z=0$ using the cloud-in-cell scheme performed by Pylians. Here we consider six threshold levels, $\vartheta =\{2.0, 1.0, 0.5, 0.3, 0.0, -0.2\}$ in such that $\delta(\boldsymbol{r},z=0)\ge \vartheta$. To smooth the constructed density field, we use the Gaussian window function with smoothing scale $R=5$ Mpc $h^{-1}$.
• Figure 3: The extracted persistence diagram of a fiducial realization from Quijote simulations. The upper left panel reveals the persistence diagram in the scatter plot for $0$-, $1$- and $2$-holes. The $\beta_k$ as a function of density threshold ($1+\delta$) is represented in the upper right panel. The complementary representations of the persistence diagram, namely $B_k$ and $P_k$ are indicated in the lower left and lower right panels, respectively. It is worth mentioning that the $\vartheta$ for the $B_k$ and $P_k$ quantifies respectively the birth and persistency thresholds.
• Figure 4: The PH vectorization for the $m$ field when the massive neutrinos particles with the total mass $M^{++}_{\nu} = 0.2 \ \rm eV$ are added compared to the fiducial cosmology. The left panels represents the Betti curves divided by the corresponding maximum value in the fiducial case. The middle and right panels are devoted to the differences in the $(B_k,P_k)$ with respect to fiducial cosmology, respectively. The blue solid, orange dashed and green dashed-dotted lines represent the 0-hole, 1-hole, and 2-hole homology groups, respectively. The shaded areas are associated with the $2\sigma$ confidence interval errors estimated over $200$ realizations. The upper and lower rows are devoted to smoothing scales $R=5$ Mpc $h^{-1}$ and $R=10$ Mpc $h^{-1}$, respectively.
• Figure 5: Same as Fig. \ref{['fig:F3_new']} just for the $cb$ part of simulated field.