We present sCOLA -- an extension of the N-body COmoving Lagrangian Acceleration (COLA) method to the spatial domain. Similar to the original temporal-domain COLA, sCOLA is an N-body method for solving for large-scale structure in a frame that is como
ving with observers following trajectories calculated in Lagrangian Perturbation Theory. Incorporating the sCOLA method in an N-body code allows one to gain computational speed by capturing the gravitational potential from the far field using perturbative techniques, while letting the N-body code solve only for the near field. The far and near fields are completely decoupled, effectively localizing gravity for the N-body side of the code. Thus, running an N-body code for a small simulation volume using sCOLA can reproduce the results of a standard N-body run for the same small volume embedded inside a much larger simulation. We demonstrate that sCOLA can be safely combined with the original temporal-domain COLA. sCOLA can be used as a method for performing zoom-in simulations. It also allows N-body codes to be made embarrassingly parallel, thus allowing for efficiently tiling a volume of interest using grid computing. Moreover, sCOLA can be useful for cheaply generating large ensembles of accurate mock halo catalogs required to study galaxy clustering. Surveys that will benefit the most are ones with large aspect ratios, such as pencil-beam surveys, where sCOLA can easily capture the effects of large-scale transverse modes without the need to substantially increase the simulated volume. As an illustration of the method, we present proof-of-concept zoom-in simulations using a freely available sCOLA-based N-body code.
We present a general method for accelerating by more than an order of magnitude the convolution of pixelated functions on the sphere with a radially-symmetric kernel. Our method splits the kernel into a compact real-space component and a compact sphe
rical harmonic space component. These components can then be convolved in parallel using an inexpensive commodity GPU and a CPU. We provide models for the computational cost of both real-space and Fourier space convolutions and an estimate for the approximation error. Using these models we can determine the optimum split that minimizes the wall clock time for the convolution while satisfying the desired error bounds. We apply this technique to the problem of simulating a cosmic microwave background (CMB) anisotropy sky map at the resolution typical of the high resolution maps produced by the Planck mission. For the main Planck CMB science channels we achieve a speedup of over a factor of ten, assuming an acceptable fractional rms error of order 1.e-5 in the power spectrum of the output map.
A small deviation from scale invariance in the form of oscillations in the primordial correlation spectra has been predicted by various cosmological models. In this paper we review a recently developed method to search for these features in the data
in a more effective way. By Taylor expanding the small features around the background cosmology, we have shown we are able to improve the search for these features compared to previous analyses. In this short paper we will extend that work by combining this method with a multi nested sampler. We recover our previous findings and are able to do so in 192 CPU hours. We will also briefly discuss the possibility of a long wavelength feature in the data to alleviate some tension between CMB data and the LCDM+r concordance cosmology.
Taking N-body simulations with volumes and particle densities tuned to match the SDSS DR7 spectroscopic main sample, we assess the ability of current void catalogs (e.g., Sutter et al. 2012b) to distinguish a model of coupled dark matter-dark energy
from {Lambda}CDM cosmology using properties of cosmic voids. Identifying voids with the VIDE toolkit, we find no statistically significant differences in the ellipticities, but find that coupling produces a population of significantly larger voids, possibly explaining the recent result of Tavasoli et al. (2013). In addition, we use the universal density profile of Hamaus et al. (2014) to quantify the relationship between coupling and density profile shape, finding that the coupling produces broader, shallower, undercompensated profiles for large voids by thinning the walls between adjacent medium-scale voids. We find that these differences are potentially measurable with existing void catalogs once effects from survey geometries and peculiar velocities are taken into account.
We perform an Alcock-Paczynski test using stacked cosmic voids identified in the SDSS Data Release 7 main sample and Data Release 10 LOWZ and CMASS samples. We find ~1,500 voids out to redshift $0.6$ using a heavily modified and extended version of t
he watershed algorithm ZOBOV, which we call VIDE (Void IDentification and Examination). To assess the impact of peculiar velocities we use the mock void catalogs presented in Sutter et al. (2013). We find a constant uniform flattening of 14% along the line of sight when peculiar velocities are included. This flattening appears universal for all void sizes at all redshifts and for all tracer densities. We also use these mocks to identify an optimal stacking strategy. After correcting for systematic effects we find that our Alcock-Paczynski measurement leads to a preference of our best-fit value of $Omega_{rm M}sim 0.15$ over $Omega_{rm M} = 1.0$ by a likelihood ratio of 10. Likewise, we find a factor of $4.5$ preference of the likelihood ratio for a $Lambda$CDM $Omega_{rm M} = 0.3$ model and a null measurement. Taken together, we find substantial evidence for the Alcock-Paczynski signal in our sample of cosmic voids. Our assessment using realistic mocks suggests that measurements with future SDSS releases and other surveys will provide tighter cosmological parameter constraints. The void-finding algorithm and catalogs used in this work will be made publicly available at http://www.cosmicvoids.net.
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.
We present and study cosmic voids identified using the watershed void finder VIDE in the Sloan Digital Sky Survey Data Release 9, compare these voids to ones identified in mock catalogs, and assess the impact of the survey mask on void statistics suc
h as number functions, ellipticity distributions, and radial density profiles. The nearly 1,000 identified voids span three nearly volume-limited samples from redshift z = 0.43 to 0.7. For comparison we use 98 of the publicly available 2LPT-based mock galaxy catalogs of Manera et al., and also generate our own mock catalogs by applying a Halo Occupation Distribution model to an N-body simulation. We find that the mask reduces the number density of voids at all scales by a factor of three and slightly skews the relative size distributions. This engenders an increase in the mean ellipticity by roughly 30%. However, we find that radial density profiles are largely robust to the effects of the mask. We see excellent agreement between the data and both mock catalogs, and find no tension between the observed void properties and the properties derived from {Lambda}CDM simulations. We have added the void catalogs from both data and mock galaxy populations discussed in this work to the Public Cosmic Void Catalog at http://www.cosmicvoids.net.
We apply our recently developed code to search for resonance features in the Planck CMB temperature data. We search both for log spaced oscillations or linear spaced oscillations and compare our findings with results of our WMAP9 analysis and the Pla
nck team analysis. While there are hints of log spaced resonant features present in the WMAP9 data, the significance of these features weaken with more data. With more accurate small scale measurements, we also find that the best fit frequency has shifted and the amplitude has been reduced. We confirm the presence of a several low frequency peaks, earlier identified by the Planck team, but with a better improvement of fit (delta chi^2 ~ 12). We further investigate this improvement by allowing the lensing potential to vary as well, showing mild correlation between the amplitude of the oscillations and the lensing amplitude. We find that the improvement of the fit increases even more (delta chi^2 ~ 14) for the low frequencies that modify the spectrum in a way that mimics the lensing effect. Since these features were not present in the WMAP data, they are primarily due to better measurements of Planck at small angular scales. For linear spaced oscillations we find a maximum delta chi^2 ~ 13 scanning two orders of magnitude in frequency space, and the biggest improvements are at extremely high frequencies. We recover a best fit frequency very close to the one found in WMAP9, which confirms that the fit improvement is driven by low l. Further comparisons with WMAP9 show Planck contains many more features, both for linear and log space oscillations, but with a smaller improvement of fit. We discuss the improvement as a function of the number of modes and study the effect of the 217 GHz map, which appears to drive most of the improvement for log spaced oscillations. We conclude that none of the detected features are statistically significant.
In this first of two papers, we present a new method for searching for oscillatory features in the primordial power spectrum. A wide variety of models predict these features in one of two different flavors: logarithmically spaced oscillations and lin
early spaced oscillations. The proposed method treats the oscillations as perturbations on top of the scale-invariant power spectrum, allowing us to vary all cosmological parameters. This perturbative approach reduces the computational requirements for the search as the transfer functions and their derivatives can be precomputed. We show that the most significant degeneracy in the analysis is between the distance to last scattering and the overall amplitude at low frequencies. For models with logarithmic oscillations, this degeneracy leads to an uncertainty in the phase. For linear spaced oscillations, it affects the frequency of the oscillations. In this first of two papers, we test our code on simulated Planck-like data, and show we are able to recover fiducial input oscillations with an amplitude of a few times order 10^{-2}. We apply the code to WMAP9-year data and confirm the existence of two intriguing resonant frequencies for log spaced oscillations. For linear spaced oscillations we find a single resonance peak. We use numerical simulations to assess the significance of these features and conclude that the data do not provide compelling evidence for the existence of oscillatory features in the primordial spectrum.
Galaxy bias, the unknown relationship between the clustering of galaxies and the underlying dark matter density field is a major hurdle for cosmological inference from large-scale structure. While traditional analyses focus on the absolute clustering
amplitude of high-density regions mapped out by galaxy surveys, we propose a relative measurement that compares those to the underdense regions, cosmic voids. On the basis of realistic mock catalogs we demonstrate that cross correlating galaxies and voids opens up the possibility to calibrate galaxy bias and to define a static ruler thanks to the observable geometric nature of voids. We illustrate how the clustering of voids is related to mass compensation and show that volume-exclusion significantly reduces the degree of stochasticity in their spatial distribution. Extracting the spherically averaged distribution of galaxies inside voids from their cross correlations reveals a remarkable concordance with the mass-density profile of voids.
