Gaussian Random-phase Initial Conditions Research Articles

A TOPOLOGICAL ANALYSIS OF LARGE-SCALE STRUCTURE, STUDIED USING THE CMASS SAMPLE OF SDSS-III

We study the three-dimensional genus topology of large-scale structure using the northern region of the CMASS Data Release 10 (DR10) sample of the SDSS-III Baryon Oscillation Spectroscopic Survey. We select galaxies with redshift 0.452 1011.56 M ☉. We study the topology at two smoothing lengths: R G = 21 h –1 Mpc and R G = 34 h –1 Mpc. The genus topology studied at the R G = 21 h –1 Mpc scale results in the highest genus amplitude observed to date. The CMASS sample yields a genus curve that is characteristic of one produced by Gaussian random phase initial conditions. The data thus support the standard model of inflation where random quantum fluctuations in the early universe produced Gaussian random phase initial conditions. Modest deviations in the observed genus from random phase are as expected from shot noise effects and the nonlinear evolution of structure. We suggest the use of a fitting formula motivated by perturbation theory to characterize the shift and asymmetries in the observed genus curve with a single parameter. We construct 54 mock SDSS CMASS surveys along the past light cone from the Horizon Run 3 (HR3) N-body simulations, where gravitationally bound dark matter subhalos are identified as the sites of galaxy formation. We study the genus topology of the HR3 mock surveys with the same geometry and sampling density as the observational sample and find the observed genus topology to be consistent with ΛCDM as simulated by the HR3 mock samples. We conclude that the topology of the large-scale structure in the SDSS CMASS sample is consistent with cosmological models having primordial Gaussian density fluctuations growing in accordance with general relativity to form galaxies in massive dark matter halos.

THREE-DIMENSIONAL GENUS TOPOLOGY OF LUMINOUS RED GALAXIES

We measure the 3D genus topology of large scale structure using Luminous Red Galaxies (LRGs) in the Sloan Digital Sky Survey and find it consistent with the Gaussian random phase initial conditions expected from the simplest scenarios of inflation. This studies 3D topology on the largest scales ever obtained. The topology is sponge-like. We measure topology in two volume-limited samples: a dense shallow sample studied with smoothing length of 21h^{-1}Mpc, and a sparse deep sample studied with a smoothing length of 34h^{-1}Mpc. The amplitude of the genus curve is measured with 4% uncertainty. Small distortions in the genus curve expected from non-linear biasing and gravitational effects are well explained (to about 1-\sigma accuracy) by N-body simulations using a subhalo-finding technique to locate LRGs. This suggests the formation of LRGs is a clean problem that can be modeled well without any free fitting parameters. This bodes well for using LRGs to measure the characteristic scales such as the baryon oscillation scale in future deep redshift surveys.

Genus Topology of Structure in the Sloan Digital Sky Survey: Model Testing

We measure the three-dimensional topology of large-scale structure in the Sloan Digital Sky Survey (SDSS). This allows the genus statistic to be measured with unprecedented statistical accuracy. The sample size is now sufficiently large to allow the topology to be an important tool for testing galaxy formation models. For comparison, we make mock SDSS samples using several state-of-the-art N-body simulations: the Millennium run of Springel et al. (10 billion particles), the Kim & Park CDM models (1.1 billion particles), and the Cen & Ostriker hydrodynamic code models (8.6 billion cell hydro mesh). Each of these simulations uses a different method for modeling galaxy formation. The SDSS data show a genus curve that is broadly characteristic of that produced by Gaussian random-phase initial conditions. Thus, the data strongly support the standard model of inflation where Gaussian random-phase initial conditions are produced by random quantum fluctuations in the early universe. But on top of this general shape there are measurable differences produced by nonlinear gravitational effects and biasing connected with galaxy formation. The N-body simulations have been tuned to reproduce the power spectrum and multiplicity function but not topology, so topology is an acid test for these models. The data show a meatball shift (only partly due to the Sloan Great Wall of galaxies) that differs at the 2.5 ? level from the results of the Millenium run and the Kim & Park dark halo models, even including the effects of cosmic variance.

Genus topology of the cosmic microwave background from the WMAP 3-year data

We have independently measured the genus topology of the temperature fluctuations in the cosmic microwave background seen in the Wilkinson Microwave Anisotropy Probe (WMAP) 3-year data. A genus analysis of the WMAP data indicates consistency with Gaussian random-phase initial conditions, as predicted by standard inflation. We set 95% confidence limits on non-linearities of -101 < f_{nl} < 107. We also find that the observed low l (l <= 8) modes show a slight anti-correlation with the Galactic foreground, but not exceeding 95% confidence, and that the topology defined by these modes is consistent with that of a Gaussian random-phase distribution (within 95% confidence).

Effects of Gravitational Evolution, Biasing, and Redshift Space Distortion on Topology

We have studied the dependence of topology of large-scale structure on tracer, gravitational evolution, redshift space distortion, and cosmology. A series of large N-body simulations of the ΛCDM and SCDM models that have evolved 1.1 or 8.6 billion particles are used in the study. Evolution of the genus statistic, used as a topology measure, from redshift 8 to 0 is accurately calculated over a wide range of smoothing scales using the simulations. The tracers of large-scale structure considered are the cold dark matter (CDM), biased peaks in the initial density field, dark halos, and populating the dark halos in accordance with a halo occupation distribution (HOD) model. We have found that the effects of biasing, gravitational evolution, and initial conditions on topology of large-scale structure are all comparable. The redshift space distortion effects are relatively small down to about 5 h-1 Mpc for all tracers except for the high-threshold part of the genus curve. The gravitational effects are found to be well modeled by analytic perturbation theory when the CDM distribution is considered. But the direction of gravitational evolution of topology can be even reversed for different tracers. For example, the shift parameter of the genus curve evolves in opposite directions for matter and HOD galaxies at large scales. At small scales, there are interesting deviations of the genus curve of dark halos and galaxies from that of matter in our initially Gaussian simulations. The deviations should be understood as due to combined effects of gravitational evolution and biasing. This fact gives us an important opportunity: topology of large-scale structure can be used as a strong constraint on galaxy formation mechanisms. At scales larger than 20 h-1 Mpc all the above effects gradually decrease. With good knowledge of the effects of nonlinear gravitational evolution and galaxy biasing on topology, one can also constrain the Gaussian random phase initial conditions hypothesis to high accuracy.

Genus topology of the cosmic microwave background from WMAP

We have independently measured the genus topology of the temperature fluctuations in the cosmic microwave background seen by the Wilkinson Microwave Anisotropy Probe (WMAP). A genus analysis of the WMAP data indicates consistency with Gaussian random-phase initial conditions, as predicted by standard inflation.

Phase information and the evolution of cosmological density perturbations

The Fourier transform of cosmological density perturbations can be represented in terms of amplitudes and phases for each Fourier mode. We investigate the phase evolution of these modes using a mixture of analytical and numerical techniques. Using a toy model of one-dimensional perturbations evolving under the Zel’dovich approximation as an initial motivation, we develop a statistic that quantifies the information content of the distribution of phases. Using numerical simulations beginning with more realistic Gaussian random-phase initial conditions, we show that the information content of the phases grows from zero in the initial conditions, first slowly and then rapidly when structures become non-linear. This growth of phase information can be expressed in terms of an effective entropy. Gaussian initial conditions are a maximum entropy realization of the initial power spectrum; gravitational evolution decreases the phase entropy. We show that our definition of phase entropy results in a statistic that explicitly quantifies the information stored in the phases of density perturbations (rather than their amplitudes), and that this statistic displays interesting scaling behaviour for self-similar initial conditions.

Cosmic Microwave Background Anisotropy Correlation Function and Topology from Simulated Maps forMAP

We have simulated cosmic microwave background (CMB) anisotropy maps for several COBE-Differential Microwave Radiometer experiment normalized cold dark matter (CDM) cosmogonies, to make predictions for the MAP experiment, an upcoming whole-sky CMB anisotropy space mission. We have studied the sensitivity of the simulated MAP data to cosmology, sky coverage, and instrumental noise. Given an accurate knowledge of instrumental noise, MAP data will ably discriminate among the cosmogonies considered, and superbly determine the topology of the initial fluctuations. A correlation function analysis of the simulated MAP data results in a very accurate measurement of the acoustic Hubble radius at decoupling. A low-density open CDM model with Ω0 = 0.4 can be distinguished from the Ω0 = 1 fiducial CDM model or a spatially flat CDM model with a cosmological constant and Ω0 = 0.4 with more than 99% confidence from the location of the acoustic valley in the correlation function. A genus analysis of the simulated MAP data indicates that in cosmogonies with Gaussian random-phase initial conditions, the horizontal shift of the zero-crossing point of the genus curve near the mean temperature threshold level ν = 0 should not exceed |Δν| = 0.01 (0.04) when the total effective FWHM smoothing is 03 (10). The asymmetry of the genus curve at the positive and negative threshold levels should not exceed |Δg/g(ν = ±1)| = 0.8% (4%) at 03 (1°) FWHM smoothing. Deviations of the observed MAP data in excess of these small values will be evidence for non-Gaussian behavior. The amplitude of the genus curve is a measure of the shape of the power spectrum at the smoothing scale. Even with the expected amount of instrumental noise and partial sky coverage (due to the Galaxy), the MAP data should allow discrimination among the cosmogonies considered at more than 99% confidence solely from a genus amplitude analysis.

The genus curve of the Abell clusters

We study the topology of large-scale structure through a genus curve measurement of the recent Abell catalog redshift survey of Postman, Huchra, and Geller (1992). The structure is found to be spongelike near median density and to exhibit isolated superclusters and voids at high and low densities, respectively. The genus curve shows a slight shift toward 'meatball' topology, but remains consistent with the hypothesis of Gaussian random phase initial conditions. The amplitude of the genus curve corresponds to a power-law spectrum with index n = 0.21(sub -0.47 sup +0.43) on scales of 48/h Mpc or to a cold dark matter power spectrum with omega h = 0.36(sub -0.17 sup +0.46).