Low density regions, called voids, occupy more than half of the Universe volume. The first observational evidence of giant voids appeared more than 30 years ago [M. Joeveer, J. Einasto, and E. Tago, MNRAS, 185, 357 (1978), S. A. Gregory and L. A. Thompson, ApJ, 222, 784 (1978) ]. The concept of cosmic voids was implemented in common practice just with coming of large spectroscopic surveys.
The sizes of voids cover a wide range of scales from the supervoids with the diameters of about 200 Mpc [U. Lindner, J. Einasto, M. Einasto, et al., A&A, 301, 329 (1995). ] to mini-voids with diameters about 3–5 Mpc [A. V. Tikhonov and I. D. Karachentsev, ApJ, 653, 969 (2006)].
Voids are important for modern astrophysics in different aspects:
- the largest dark energy dominated objects,
- highways for energetic particles: electromagnetic cascades, UHECRs, neutrinos,
- modified extragalactic background light and magnetic field,
- the sites of very isolated galaxies (void population),
- convenient tool for cosmological probes (Alcock-Paczynski test).
Cosmic voids are one of the most promising observational probes to discriminate between alternative models of the Universe. Among several interesting applications, it has been shown that cosmic voids can be efficiently used for the Alcock–Paczyski (AP) test [Alcock, C., & Paczynski, B. 1979, Nature, 281, 358 ], by measuring the ratio between their sizes along and perpendicular to the line of sight. When many voids are stacked together, the resulting average void is expected to be spherical in an isotropic Universe. Stacked void appears anisotropic at adopting of incorrect space-time metric [Sutter P.M., Lavaux G., Wandelt B.D., Weinberg D.H. 2012, ApJ, 761, 187]. Hence, constraints on cosmological parameters can be obtained by measuring the stretched shape of the staked void in a redshift-space.
In literature we may find many void finders which are compared in the Aspen-Amsterdam void finder comparison project [Colberg, J.M., Pearce F., Foster C., et al. 2008, MNRAS, 387, 933]. All void finders use different approaches and could be divided on 4 main types:
- density smoothing, looking for the local minimum, Colberg et al. 2005, Pearce et al. 2007, Plionis et al. 2002, Shandarin et al. 2006
- looking for the empty spheres (put link on second part), or for regions with a galaxy density below a given threshold, Brunino et al. 2007, Colberg et al. 2005, Muller et al. 2000, Gottlober et al. 2003, Elyiv et al. 2013
- Voronoi and Delaunay tesselations, Neyrinck 2008, Platen et al. 2007
- test particle motion in smoothed gravitational field, Hahn et al. 2006
An accurate measurement of void shapes and their centers is crucial for the AP test. By definition, the voids are cosmic regions free of galaxies. Alternatively, they can be defined as regions with a galaxy density below a given threshold. Void identification algorithms are generally based on density measurements. However, as the density in void environments is low, its measurement is severely affected by shot noise. This represents one of the main weaknesses of these methods. Other problem for many void finders is smoothing of density field. In result voids become more spherical which is significant bias for AP test.
A few points from the dynamics of voids [Aragon-Calvo M.A., Szalay A.S. 2013, MNRAS, 428, 3409] are critically important at the construction of void finder for AP test:
- voids are not regular spheres except isolated ones;
- voids have the complicate hierarchical structure with division on subvoids;
- the velocity field inside voids depends on the density as δ∞-div v, which means that inner regions expand faster than outer shells;
- In the low-density environment the fluctuations grow in the linear regime and the velocity field is coherent laminar flow