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Voids have emerged as a novel probe of cosmology and large-scale structure. These regions of extreme underdensity are sensitive to physics beyond the standard model of cosmology, and can potentially be used as a testing ground to constrain new physics. We present the first determination of the linear void bias measured in separate universe simulations. Our methods are validated by comparing the separate universe response bias with the clustering bias of voids. We find excellent agreement between the two methods for voids identified in the halo field and the down-sampled dark matter field. For voids traced by halos, we identify two different contributions to the bias. The first is due to the bias of the underlying halo field used to identify voids, while the second we attribute to the dynamical impact of long-wavelength density perturbations on void formation and expansion. By measuring these contributions individually, we demonstrate that their sum is consistent with the total void bias. We also measure the void profiles in our simulations, and determine their separate universe response. These can be interpreted as the sensitivity of the profiles to the background density of the Universe.
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Cosmic voids are biased tracers of the large-scale structure of the universe. Separate universe simulations (SUS) enable accurate measurements of this biasing relation by implementing the peak-background split (PBS). In this work, we apply the SUS technique to measure the void bias parameters. We confirm that the PBS argument works well for underdense tracers. The response of the void size distribution depends on the void radius. For voids larger (smaller) than the size at the peak of the distribution, the void abundance responds negatively (positively) to a long wavelength mode. The linear bias from the SUS is in good agreement with the cross power spectrum measurement on large scales. Using the SUS, we have detected the quadratic void bias for the first time in simulations. We find that $ b_2 $ is negative when the magnitude of $ b_1 $ is small, and that it becomes positive and increases rapidly when $ |b_1| $ increases. We compare the results from voids identified in the halo density field with those from the dark matter distribution, and find that the results are qualitatively similar, but the biases generally shift to the larger voids sizes.
We study the evolution of linear density perturbations in a large spherical void universe which accounts for the acceleration of the cosmic volume expansion without introducing dark energy. The density contrast of this void is not large within the light cone of an observer at the center of the void. Therefore, we describe the void structure as a perturbation with a dimensionless small parameter $kappa$ in a homogeneous and isotropic universe within the region observable for the observer. We introduce additional anisotropic perturbations with a dimensionless small parameter $epsilon$, whose evolution is of interest. Then, we solve perturbation equations up to order $kappa epsilon$ by applying second-order perturbation theory in the homogeneous and isotropic universe model. By this method, we can know the evolution of anisotropic perturbations affected by the void structure. We show that the growth rate of the anisotropic density perturbations in the large void universe is significantly different from that in the homogeneous and isotropic universe. This result suggests that the observation of the distribution of galaxies may give a strong constraint on the large void universe model.
We analyse the clustering of cosmic voids using a numerical simulation and the main galaxy sample from the Sloan Digital Sky Survey. We take into account the classification of voids into two types that resemble different evolutionary modes: those with a rising integrated density profile (void-in-void mode, or R-type) and voids with shells (void-in-cloud mode, or S-type). The results show that voids of the same type have stronger clustering than the full sample. We use the correlation analysis to define void clumps, associations with at least two voids separated by a distance of at most the mean void separation. In order to study the spatial configuration of void clumps, we compute the minimal spanning tree and analyse their multiplicity, maximum length and elongation parameter. We further study the dynamics of the smaller sphere that encloses all the voids in each clump. Although the global densities of void clumps are different according to their member-void types, the bulk motions of these spheres are remarkably lower than those of randomly placed spheres with the same radii distribution. In addition, the coherence of pairwise void motions does not strongly depend on whether voids belong to the same clump. Void clumps are useful to analyse the large-scale flows around voids, since voids embedded in large underdense regions are mostly in the void-in-void regime, were the expansion of the larger region produces the separation of voids. Similarly, voids around overdense regions form clumps that are in collapse, as reflected in the relative velocities of voids that are mostly approaching.
Luminous tracers of large-scale structure are not entirely representative of the distribution of mass in our Universe. As they arise from the highest peaks in the matter density field, the spatial distribution of luminous objects is biased towards those peaks. On large scales, where density fluctuations are mild, this bias simply amounts to a constant offset in the clustering amplitude of the tracer, known as linear bias. In this work we focus on the relative bias between galaxies and galaxy clusters that are located inside and in the vicinity of cosmic voids, extended regions of relatively low density in the large-scale structure of the Universe. With the help of hydro-dynamical simulations we verify that the relation between galaxy and cluster overdensity around voids remains linear. Hence, the void-centric density profiles of different tracers can be linked by a single multiplicative constant. This amounts to the same value as the relative linear bias between tracers for the largest voids in the sample. For voids of small sizes, which typically arise in higher density regions, this constant has a higher value, possibly showing an environmental dependence similar to that observed for the linear bias itself. We confirm our findings by analysing mocks and data obtained during the first year of observations by the Dark Energy Survey. As a side product, we present the first catalogue of three-dimensional voids extracted from a photometric survey with a controlled photo-z uncertainty. Our results will be relevant in forthcoming analyses that attempt to use voids as cosmological probes.
We study the two-point correlation function of density perturbations in a spherically symmetric void universe model which does not employ the Copernican principle. First we solve perturbation equations in the inhomogeneous universe model and obtain density fluctuations by using a method of non-linear perturbation theory which was adopted in our previous paper. From the obtained solutions, we calculate the two-point correlation function and show that it has a local anisotropy at the off-center position differently from those in homogeneous and isotropic universes. This anisotropy is caused by the tidal force in the off-center region of the spherical void. Since no tidal force exists in homogeneous and isotropic universes, we may test the inhomogeneous universe by observing statistical distortion of the two-point galaxy correlation function.
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