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Abstract. Cosmic voids are a promising environment to characterize neutrino-induced effects on the large-scale distribution of matter in the universe. We perform a comprehensive numerical study of the statistical properties of voids, identified both in the matter and galaxy distributions, in massive and massless neutrino cosmologies. The matter density field is obtained by running several independent N -body simulations with cold dark matter and neutrino particles, while the galaxy catalogs are modeled by populating the dark matter halos in simulations via a halo occupation distribution (HOD) model to reproduce the clustering properties observed by the Sloan Digital Sky Survey (SDSS) II Data Release 7. We focus on the impact of massive neutrinos on the following void statistical properties: number density, ellipticities, two-point statistics, density and velocity profiles. Considering the matter density field, we find that voids in massive neutrino cosmologies are less evolved than those in the corresponding massless neutrinos case: there is a larger number of small voids and a smaller number of large ones, their profiles are less evacuated, and they present a lower wall at the edge. Moreover, the degeneracy between σ 8 and Ω ν is broken when looking at void properties. In terms of the galaxy density field, we find that differences among cosmologies are difficult to detect because of the small number of galaxy voids in the simulations. Differences are instead present when looking at the matter density and velocity profiles around these voids.

Do void statistics contain information beyond the tracer 2-point correlation function? Yes! As we vary the sum of the neutrino masses, we find void statistics contain information absent when using just tracer 2-point statistics. Massive neutrinos uniquely affect cosmic voids. We explore their impact on void clustering using both the DEMNUni and MassiveNuS simulations. For voids, neutrino effects depend on the observed void tracers. As the neutrino mass increases, the number of small voids traced by cold dark matter particles increases and the number of large voids decreases. Surprisingly, when massive, highly biased, halos are used as tracers, we find the opposite effect. The scale at which voids cluster, as well as the void correlation, is similarly sensitive to the sum of neutrino masses and the tracers. This scale dependent trend is not due to simulation volume or halo density. The interplay of these signatures in the void abundance and clustering leaves a distinct fingerprint that could be detected with observations and potentially help break degeneracies between different cosmological parameters. This paper paves the way to exploit cosmic voids in future surveys to constrain the mass of neutrinos.

Cosmological neutrinos have their greatest influence in voids: these are the regions with the highest neutrino to dark matter density ratios. The marked power spectrum can be used to emphasize low density regions over high density regions, and therefore is potentially much more sensitive than the power spectrum to the effects of neutrino masses. Using 22,000 N-body simulations from the Quijote suite, we quantify the information content in the marked power spectrum of the matter field, and show that it outperforms the standard power spectrum by setting constraints improved by a factor larger than 2 on all cosmological parameters. The combination of marked and standard power spectrum allows to place a 4.3σ constraint on the minimum sum of the neutrino masses with a volume equal to 1 (Gpc h −1 ) 3 and without CMB priors. Combinations of different marked power spectra yield a 6σ constraint within the same conditions.

Abstract. We provide a quantitative analysis of the halo model in the context of massive neutrino cosmologies. We discuss all the ingredients necessary to model the non-linear matter and cold dark matter power spectra and compare with the results of N-body simulations that incorporate massive neutrinos. Our neutrino halo model is able to capture the nonlinear behavior of matter clustering with a ∼ 20% accuracy up to very non-linear scales of k = 10 h/Mpc (which would be affected by baryon physics). The largest discrepancies arise in the range k = 0.5 − 1 h/Mpc where the 1-halo and 2-halo terms are comparable and are present also in a massless neutrino cosmology. However, at scales k < 0.2 h/Mpc our neutrino halo model agrees with the results of N-body simulations at the level of 8% for total neutrino masses of < 0.3 eV. We also model the neutrino non-linear density field as a sum of a linear and clustered component and predict the neutrino power spectrum and the cold dark matter-neutrino cross-power spectrum up to k = 1 h/Mpc with ∼ 30% accuracy. For masses below 0.15 eV the neutrino halo model captures the neutrino induced suppression, casted in terms of matter power ratios between massive and massless scenarios, with a 2% agreement with the results of N-body/neutrino simulations. Finally, we provide a simple application of the halo model: the computation of the clustering of galaxies, in massless and massive neutrinos cosmologies, using a simple Halo Occupation Distribution scheme and our halo model extension.

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We quantify the information content of the nonlinear matter power spectrum, the halo mass function, and the void size function, using the Quijote N-body simulations. We find that these three statistics exhibit very different degeneracies among the cosmological parameters, and thus the combination of all three probes enables the breaking of degeneracies, in turn yielding remarkably tight constraints. We perform a Fisher analysis using the full covariance matrix, including all auto- and cross correlations, finding that this increases the information content for neutrino mass compared to a correlation-free analysis. The multiplicative improvement of the constraints on the cosmological parameters obtained by combining all three probes compared to using the power spectrum alone are: 137, 5, 8, 20, 10, and 43, for Ω m , Ω b , h, n s , σ 8, and M ν , respectively. The marginalized error on the sum of the neutrino masses is σ(M ν ) = 0.018 eV for a cosmological volume of 1 h − 1 Gpc 3 , using k max = 0.5 h Mpc − 1 , and without cosmic microwave background (CMB) priors. We note that this error is an underestimate insomuch as we do not consider super-sample covariance, baryonic effects, and realistic survey noises and systematics. On the other hand, it is an overestimate insomuch as our cuts and binning are suboptimal due to restrictions imposed by the simulation resolution. Given upcoming galaxy surveys will observe volumes spanning ∼ 100 h − 1 Gpc 3 , this presents a promising new avenue to measure neutrino mass without being restricted by the need for accurate knowledge of the optical depth, which is required for CMB-based measurements. Furthermore, the improved constraints on other cosmological parameters, notably Ω m , may also be competitive with CMB-based measurements.

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