ALBERT

Description: We explore voids in dark matter and halo fields from simulations of cold dark matter and Hu–Sawicki f ( R ) models. In f ( R ) gravity, dark matter void abundances are greater than that of general relativity (GR). Differences for halo void abundances are much smaller, but still at the 2, 6 and 14 level for the f ( R ) model parameter | f R 0 | = 10 –6 , 10 –5 and 10 –4 . Counter-intuitively, the abundance of large voids found using haloes in f ( R ) gravity is lower, which suggests that voids are not necessarily emptier of galaxies in this model. We find the halo number density profiles of voids are not distinguishable from GR, but the same voids are emptier of dark matter in f ( R ) gravity. This can be observed by weak gravitational lensing of voids, for which the combination of a spec- z and a photo- z survey over the same sky is necessary. For a volume of 1 (Gpc  h –1 ) 3 , | f R 0 | = 10 –5 and 10 –4 may be distinguished from GR at 4 and 8 using the lensing tangential shear signal around voids. Sample variance and line-of-sight projection effect sets limits for constraining | f R 0 | = 10 –6 . This might be overcome with a larger volume. The smaller halo void abundance and the stronger lensing shear signal of voids in f ( R ) models may be combined to break the degeneracy between | f R 0 | and 8 . The outflow of dark matter from void centres are 5, 15 and 35 per cent faster in f ( R ) gravity for | f R 0 | = 10 –6 , 10 –5 and 10 –4 . The velocity dispersions are greater than that in GR by similar amounts. Model differences in velocities imply potential powerful constraints for the model in phase space and in redshift space.

Description: We investigate the behaviour of the fifth force in voids in chameleon models using the spherical collapse method. Contrary to Newtonian gravity, we find the fifth force is repulsive in voids. The strength of the fifth force depends on the density inside and outside the void region as well as its radius. It can be many times larger than the Newtonian force and their ratio is in principle unbound. This is very different from the case in haloes, where the fifth force is no more than 1/3 of gravity. The evolution of voids is governed by the Newtonian gravity, the effective dark energy force and the fifth force. While the first two forces are common in both cold dark matter (CDM) and chameleon universes, the fifth force is unique to the latter. Driven by the outward-pointing fifth force, individual voids in chameleon models expand faster and grow larger than in a CDM universe. The expansion velocity of the void shell can be 20–30 per cent larger for voids of a few Mpc  h –1 in radius, while their sizes can be larger by ~10 per cent. This difference is smaller for larger voids of the same density. We compare void statistics using excursion set theory; for voids of the same size, their number density is found to be larger in chameleon models. The fractional difference increases with void size due to the steepening of the void distribution function. The chance of having voids of radius ~25 Mpc  h –1 can be 2.5 times larger. This difference is about 10 times larger than that in the halo mass function. We find strong environmental dependence of void properties and population in chameleon models. The differences in size and expansion velocity with general relativity are both larger for small voids in high-density regions. In general, the difference between chameleon models and CDM in void properties (size, expansion velocity and distribution function) is larger than the corresponding quantities for haloes. This suggests that voids might be better candidates than haloes for testing gravity.

Description: We revisit the excursion set approach to calculate void abundances in chameleon-type modified gravity theories, which was previously studied by Clampitt, Cai & Li. We focus on properly accounting for the void-in-cloud effect, i.e. the growth of those voids sitting in overdense regions may be restricted by the evolution of their surroundings. This effect may change the distribution function of voids hence affect predictions on the differences between modified gravity (MG) and general relativity (GR). We show that the thin-shell approximation usually used to calculate the fifth force is qualitatively good but quantitatively inaccurate. Therefore, it is necessary to numerically solve the fifth force in both overdense and underdense regions. We then generalize the Eulerian-void-assignment method of Paranjape, Lam & Sheth to our modified gravity model. We implement this method in our Monte Carlo simulations and compare its results with the original Lagrangian methods. We find that the abundances of small voids are significantly reduced in both MG and GR due to the restriction of environments. However, the change in void abundances for the range of void radii of interest for both models is similar. Therefore, the difference between models remains similar to the results from the Lagrangian method, especially if correlated steps of the random walks are used. As Clampitt et al., we find that the void abundance is much more sensitive to MG than halo abundances. Our method can then be a faster alternative to N -body simulations for studying the qualitative behaviour of a broad class of theories. We also discuss the limitations and other practical issues associated with its applications.

Description: We have derived estimators for the linear growth rate of density fluctuations using the cross-correlation function (CCF) of voids and haloes in redshift space. In linear theory, this CCF contains only monopole and quadrupole terms. At scales greater than the void radius, linear theory is a good match to voids traced out by haloes; small-scale random velocities are unimportant at these radii, only tending to cause small and often negligible elongation of the CCF near its origin. By extracting the monopole and quadrupole from the CCF, we measure the linear growth rate without prior knowledge of the void profile or velocity dispersion. We recover the linear growth parameter β to 9 per cent precision from an effective volume of 3( h –1 Gpc) 3 using voids with radius 〉25 h –1 Mpc. Smaller voids are predominantly sub-voids, which may be more sensitive to the random velocity dispersion; they introduce noise and do not help to improve measurements. Adding velocity dispersion as a free parameter allows us to use information at radii as small as half of the void radius. The precision on β is reduced to 5 per cent. Voids show diverse shapes in redshift space, and can appear either elongated or flattened along the line of sight. This can be explained by the competing amplitudes of the local density contrast, plus the radial velocity profile and its gradient. The distortion pattern is therefore determined solely by the void profile and is different for void-in-cloud and void-in-void. This diversity of redshift-space void morphology complicates measurements of the Alcock–Paczynski effect using voids.

Description: We study the spherical evolution model for voids in CDM, where the evolution of voids is governed by dark energy at an earlier time than that for the whole universe or in overdensities. We show that the presence of dark energy suppresses the growth of peculiar velocities, causing void shell-crossing to occur at progressively later epochs as increases. We apply the spherical model to evolve the initial conditions of N -body simulated voids and compare the resulting final void profiles. We find that the model is successful in tracking the evolution of voids with radii greater than 30 h –1 Mpc, implying that void profiles could be used to constrain dark energy. We find that the initial peculiar velocities of voids play a significant role in shaping their evolution. Excluding the peculiar velocity in the evolution model delays the time of shell crossing.

Description: Langmuir DOI: 10.1021/la103155c

Description: We study the late-time integrated Sachs–Wolfe (ISW) effect in f ( R ) gravity using N -body simulations. In the f ( R ) model under study, the linear growth rate is larger than that in general relativity (GR). This slows down the decay of the cosmic potential and induces a smaller ISW effect on large scales. Therefore, the $\dot{\Phi }$ (time derivative of the potential) power spectrum at k  〈 0.1 h  Mpc –1 is suppressed relative to that in GR. In the non-linear regime, relatively rapid structure formation in f ( R ) gravity boosts the non-linear ISW effect relative to GR, and the $\dot{\Phi }$ power spectrum at k  〉 0.1 h  Mpc –1 is increased (100 per cent greater on small scales at z  = 0). We explore the detectability of the ISW signal via stacking supercluster and supervoids. The differences in the corresponding ISW cold- or hotspots are ~20 per cent for structures of ~100 Mpc  h –1 . Such differences are greater for smaller structures, but the amplitude of the signal is lower. The high amplitude of ISW signal detected by Granett et al. cannot be explained in the f ( R ) model. We find relatively big differences between f ( R ) and GR in the transverse bulk motion of matter, and discuss its detectability via the relative frequency shifts of photons from multiple lensed images.

Description: We introduce a new method for stacking voids and deriving their profile that greatly increases the potential of voids as a tool for precision cosmology. Given that voids are distinctly non-spherical and have most of their mass at their edge, voids are better described relative to their boundary rather than relative to their centre, as in the conventional spherical stacking approach. The boundary profile is obtained by computing the distance of each volume element from the void boundary. Voids can then be stacked and their profiles computed as a function of this boundary distance. This approach enhances the weak lensing signal of voids, both shear and convergence, by a factor of 2 when compared to the spherical stacking method. It also results in steeper void density profiles that are characterized by a very slow rise inside the void and a pronounced density ridge at the void boundary. The resulting boundary density profile is self-similar when rescaled by the thickness of the density ridge, implying that the average rescaled profile is independent of void size. The boundary velocity profile is characterized by outflows in the inner regions whose amplitude scales with void size, and by a strong inflow into the filaments and walls delimiting the void. This new picture enables a straightforward discrimination between collapsing and expanding voids both for individual objects as well as for stacked samples.