Large-Scale Clustering of Cosmic Voids

We study the clustering of voids using $N$-body simulations and simple theoretical models. The excursion-set formalism describes fairly well the abundance of voids identified with the watershed algorithm, although the void formation threshold required is quite different from the spherical collapse value. The void cross bias $b_{\rm c}$ is measured and its large-scale value is found to be consistent with the peak background split results. A simple fitting formula for $b_{\rm c}$ is found. We model the void auto-power spectrum taking into account the void biasing and exclusion effect. A good fit to the simulation data is obtained for voids with radii $\gtrsim$ 30 Mpc/$h$, especially when the void biasing model is extended to 1-loop order. However, the best-fit bias parameters do not agree well with the peak-background split results. Being able to fit the void auto-power spectrum is particularly important not only because it is the direct observable in galaxy surveys, but also our method enables us to treat the bias parameters as nuisance parameters, which are sensitive to the techniques used to identify voids.Comment: 20 pages, 14 figures, minor changes to match published versio

Constraint of Void Bias on Primordial non-Gaussianity

We study the large-scale bias parameter of cosmic voids with primordial non-Gaussian (PNG) initial conditions of the local type. In this scenario, the dark matter halo bias exhibits a characteristic scale dependence on large scales, which has been recognized as one of the most promising probes of the local PNG. Using a suite of $N$-body simulations with Gaussian and non-Gaussian initial conditions, we find that the void bias features scale-dependent corrections on large scales, similar to its halo counterpart. We find excellent agreement between the numerical measurement of the PNG void bias and the general peak-background split prediction. Contrary to halos, large voids anti-correlate with the dark matter density field, and the large-scale Gaussian void bias ranges from positive to negative values depending on void size and redshift. Thus, the information in the clustering of voids can be complementary to that of the halos. Using the Fisher matrix formalism for multiple tracers, we demonstrate that including the scale-dependent bias information from voids, constraints on the PNG parameter $f_{\rm NL}$ can be tightened by a factor of two compared to the accessible information from halos alone, when the sampling density of tracers reaches $4 \times 10^{-3} \, h^3 \mathrm{Mpc}^{-3}$.Comment: 7 pages, 4 figures; dn/dlnsigma_8 prediction implemented and excellent agreement with simulation results obtained. Matched to published versio

Universal Density Profile for Cosmic Voids

We present a simple empirical function for the average density profile of cosmic voids, identified via the watershed technique in $\Lambda$CDM N-body simulations. This function is universal across void size and redshift, accurately describing a large radial range of scales around void centers with only two free parameters. In analogy to halo density profiles, these parameters describe the scale radius and the central density of voids. While we initially start with a more general four-parameter model, we find two of its parameters to be redundant, as they follow linear trends with the scale radius in two distinct regimes of the void sample, separated by its compensation scale. Assuming linear theory, we derive an analytic formula for the velocity profile of voids and find an excellent agreement with the numerical data as well. In our companion paper [Sutter et al., Mon. Not. R. Astron. Soc. 442, 462 (2014)] the presented density profile is shown to be universal even across tracer type, properly describing voids defined in halo and galaxy distributions of varying sparsity, allowing us to relate various void populations by simple rescalings. This provides a powerful framework to match theory and simulations with observational data, opening up promising perspectives to constrain competing models of cosmology and gravity.Comment: 5 pages, 3 figures. Matches PRL published version after minor correction

Probing cosmology and gravity with redshift-space distortions around voids

Cosmic voids in the large-scale structure of the Universe affect the peculiar motions of objects in their vicinity. Although these motions are difficult to observe directly, the clustering pattern of their surrounding tracers in redshift space is influenced in a unique way. This allows to investigate the interplay between densities and velocities around voids, which is solely dictated by the laws of gravity. With the help of $N$-body simulations and derived mock-galaxy catalogs we calculate the average density fluctuations around voids identified with a watershed algorithm in redshift space and compare the results with the expectation from general relativity and the $\Lambda$CDM model. We find linear theory to work remarkably well in describing the dynamics of voids. Adopting a Bayesian inference framework, we explore the full posterior of our model parameters and forecast the achievable accuracy on measurements of the growth rate of structure and the geometric distortion through the Alcock-Paczynski effect. Systematic errors in the latter are reduced from $\sim15\%$ to $\sim5\%$ when peculiar velocities are taken into account. The relative parameter uncertainties in galaxy surveys with number densities comparable to the SDSS MAIN (CMASS) sample probing a volume of $1h^{-3}{\rm Gpc}^3$ yield $\sigma_{f/b}\left/(f/b)\right.\sim2\%$ ($20\%$) and $\sigma_{D_AH}/D_AH\sim0.2\%$ ($2\%$), respectively. At this level of precision the linear-theory model becomes systematics dominated, with parameter biases that fall beyond these values. Nevertheless, the presented method is highly model independent; its viability lies in the underlying assumption of statistical isotropy of the Universe.Comment: 38 pages, 14 figures. Published in JCAP. Referee comments incorporated, typos corrected, references added. Considerably improved results thanks to consideration of full covariance matrix in the MCMC analysi

The bias of cosmic voids in the presence of massive neutrinos

Cosmic voids offer an extraordinary opportunity to study the effects of massive neutrinos on cosmological scales. Because they are freely streaming, neutrinos can penetrate the interior of voids more easily than cold dark matter or baryons, which makes their relative contribution to the mass budget in voids much higher than elsewhere in the Universe. In simulations it has recently been shown how various characteristics of voids in the matter distribution are affected by neutrinos, such as their abundance, density profiles, dynamics, and clustering properties. However, the tracers used to identify voids in observations (e.g., galaxies or halos) are affected by neutrinos as well, and isolating the unique neutrino signatures inherent to voids becomes more difficult. In this paper we make use of the DEMNUni suite of simulations to investigate the clustering bias of voids in Fourier space as a function of their core density and compensation. We find a clear dependence on the sum of neutrino masses that remains significant even for void statistics extracted from halos. In particular, we observe that the amplitude of the linear void bias increases with neutrino mass for voids defined in dark matter, whereas this trend gets reversed and slightly attenuated when measuring the relative void-halo bias using voids identified in the halo distribution. Finally, we argue how the original behaviour can be restored when considering observations of the total matter distribution (e.g. via weak lensing), and comment on scale-dependent effects in the void bias that may provide additional information on neutrinos in the future.Comment: 23 pages, 18 figure

Why Cosmic Voids Matter: Nonlinear Structure & Linear Dynamics

We use the Magneticum suite of state-of-the-art hydrodynamical simulations to identify cosmic voids based on the watershed technique and investigate their most fundamental properties across different resolutions in mass and scale. This encompasses the distributions of void sizes, shapes, and content, as well as their radial density and velocity profiles traced by the distribution of cold dark matter particles and halos. We also study the impact of various tracer properties, such as their sparsity and mass, and the influence of void merging on these summary statistics. Our results reveal that all of the analyzed void properties are physically related to each other and describe universal characteristics that are largely independent of tracer type and resolution. Most notably, we find that the motion of tracers around void centers is perfectly consistent with linear dynamics, both for individual, as well as stacked voids. Despite the large range of scales accessible in our simulations, we are unable to identify the occurrence of nonlinear dynamics even inside voids of only a few Mpc in size. This suggests voids to be among the most pristine probes of cosmology down to scales that are commonly referred to as highly nonlinear in the field of large-scale structure.Comment: 35 pages (+ references), 22 figures. Key results in figure 22. Accepted for publication in JCA

Dark matter voids in the SDSS galaxy survey

What do we know about voids in the dark matter distribution given the Sloan Digital Sky Survey (SDSS) and assuming the $\Lambda\mathrm{CDM}$ model? Recent application of the Bayesian inference algorithm BORG to the SDSS Data Release 7 main galaxy sample has generated detailed Eulerian and Lagrangian representations of the large-scale structure as well as the possibility to accurately quantify corresponding uncertainties. Building upon these results, we present constrained catalogs of voids in the Sloan volume, aiming at a physical representation of dark matter underdensities and at the alleviation of the problems due to sparsity and biasing on galaxy void catalogs. To do so, we generate data-constrained reconstructions of the presently observed large-scale structure using a fully non-linear gravitational model. We then find and analyze void candidates using the VIDE toolkit. Our methodology therefore predicts the properties of voids based on fusing prior information from simulations and data constraints. For usual void statistics (number function, ellipticity distribution and radial density profile), all the results obtained are in agreement with dark matter simulations. Our dark matter void candidates probe a deeper void hierarchy than voids directly based on the observed galaxies alone. The use of our catalogs therefore opens the way to high-precision void cosmology at the level of the dark matter field. We will make the void catalogs used in this work available at http://www.cosmicvoids.net.Comment: 15 pages, 6 figures, matches JCAP published version, void catalogs publicly available at http://www.cosmicvoids.ne