Hume A. Feldman

Theory of cosmological perturbations

We present in a manifestly gauge-invariant form the theory of classical linear gravitational perturbations in part I, and a quantum theory of cosmological perturbations in part II. Part I includes applications to several important examples arising in cosmology: a univese dominated by hydrodynamical matter, a universe filled with scalar-field matter, and higher-derivative theories of gravity. The growth rates of perturbations are calculated analytically in most interesting cases. The analysis is applied to study the evolution of fluctuations in inflationary universe models. Part II includes a unified description of the quantum generation and evolution of inhomogeneities about a classial Friedmann background. The method is based on standard canonical quantization of the action for cosmological perturbations which has been reduced to an expression in terms of a single gauge-invariant variable. The spectrum of density perturbations originating in quantum fluctuations is calculated in universe with hydrodynamical matter, in inflationary universe models with scalar-field matter, and in higher-derivative theories of gravity. The gauge-invariant theory of classical and quantized cosmological perturbations developed in parts I and II is applied in part III to several interesting physical problems. It allows a simple derivation of the relation between temperature anistropes in the cosmic microwave background. radiation and the gauge-invariant potential for metric perturbations. The generation and evolution of gravitational waves is studied. As another example, a simple analysis of entropy perturbations and non-scale-invariant spectra in inflationary universe models is presented. The gauge-invariant theory of cosmological perturbations also allows a consistent and gauge-invariant definition of statistical fluctuations.

POWER-SPECTRUM ANALYSIS OF THREE-DIMENSIONAL REDSHIFT SURVEYS

We develop a general method for power spectrum analysis of three dimensional redshift surveys. We present rigorous analytical estimates for the statistical uncertainty in the power and we are able to derive a rigorous optimal weighting scheme under the reasonable (and largely empirically verified) assumption that the long wavelength Fourier components are Gaussian distributed. We apply the formalism to the updated 1-in-6 QDOT IRAS redshift survey, and compare our results to data from other probes: APM angular correlations; the CfA and the Berkeley 1.2Jy IRAS redshift surveys. Our results bear out and further quantify the impression from e.g.\ counts-in-cells analysis that there is extra power on large scales as compared to the standard CDM model with

Cosmic flows on 100 h−1 Mpc scales: standardized minimum variance bulk flow, shear and octupole moments

\Omega h\simeq 0.5

The Aspen–Amsterdam void finder comparison project

. We apply likelihood analysis using the CDM spectrum with

The Bispectrum of IRAS redshift catalogs

\Omega h

Constraints on Galaxy Bias, Matter Density, and Primordial Non-Gaussianity from the PSCz Galaxy Redshift Survey

as a free parameter as a phenomenological family of models; we find the best fitting parameters in redshift space and transform the results to real space. Finally, we calculate the distribution of the estimated long wavelength power. This agrees remarkably well with the exponential distribution expected for Gaussian fluctuations, even out to powers of ten times the mean. Our results thus reveal no trace of periodicity or other non-Gaussian behavior.

The Bispectrum of IRAS Galaxies

The low order moments, such as the bulk flow and shear, of the large scale peculiar velocity field are sensitive probes of the matter density fluctuations on very large scales. In practice, however, peculiar velocity surveys are usually sparse and noisy, which can lead to the aliasing of small scale power into what is meant to be a probe of the largest scales. Previously, we developed an optimal “minimum variance” (MV) weighting scheme, designed to overcome this problem by minimizing the difference between the measured bulk flow (BF) and that which would be measured by an ideal survey. Here we extend this MV analysis to include the shear and octupole moments, which are designed to have almost no correlations between them so that they are virtually orthogonal. We apply this MV analysis to a compilation of all major peculiar velocity surveys, consisting of 4536 measurements. Our estimate of the BF on scales of � 100h 1 Mpc has a magnitude of |v| = 416±78 km/s towards Galactic l = 282 o ±11 o

Shapes and sizes of voids in the Lambda cold dark matter universe: excursion set approach

Despite a history that dates back at least a quarter of a century studies of voids in the large–scale structure of the Universe are bedevilled by a major problem: there exist a large number of quite different void–finding algorithms, a fact that has so far got in the way of groups comparing their results without worrying about whether such a comparison in fact makes sense. Because of the recent increased interest in voids, both in very large galaxy surveys and in detailed simulations of cosmic structure formation, this situation is very unfortunate. We here present the first systematic comparison study of thirteen different void finders constructed using particles, haloes, and semi– analytical model galaxies extracted from a subvolume of the Millennium simulation. The study includes many groups that have studied voids over the past decade. We show their results and discuss their differences and agreements. As it turns out, the basic results of the various methods agree very well with each other in that they all locate a major void near the centre of our volume. Voids have very underdense centres, reaching below 10 percent of the mean cosmic density. In addition, those void finders that allow for void galaxies show that those galaxies follow similar trends. For example, the overdensity of void galaxies brighter than mB = 20 is found to be smaller than about 0.8 by all our void finding algorithms.

MINKOWSKI FUNCTIONALS AND CLUSTER ANALYSIS FOR CMB MAPS

We compute the bispectrum for the galaxy distribution in the IRAS QDOT, 2Jy, and 1.2Jy redshift catalogs for wavenumbers 0.05 1 at large scales, \chi^2 non-Gaussian initial conditions are ruled out at the 95% confidence level. The IRAS data do not distinguish between Lagrangian or Eulerian local bias.We compute the bispectrum for the galaxy distribution in the IRAS QDOT, 2 Jy, and 1.2 Jy redshift catalogs for wavenumbers 0.05 ≤ k ≤ 0.2 h Mpc-1 and compare the results with predictions from gravitational instability in perturbation theory. Taking into account redshift-space distortions, nonlinear evolution, the survey selection function, and discreteness and finite-volume effects, all three catalogs show evidence for the dependence of the bispectrum on the configuration shape predicted by gravitational instability. Assuming Gaussian initial conditions and local biasing parameterized by linear and nonlinear bias parameters b1 and b2, a likelihood analysis yields 1/b1 = 1.32, 1.15 and b2/b = -0.57, -0.50 for the 2 and 1.2 Jy samples, respectively. This implies that IRAS galaxies trace dark matter increasingly weakly as the density contrast increases, consistent with their being underrepresented in clusters. In a model with χ2 non-Gaussian initial conditions, the bispectrum displays an amplitude and scale dependence different from that found in the Gaussian case; if IRAS galaxies do not have bias b1 > 1 at large scales, χ2 non-Gaussian initial conditions are ruled out at the 95% confidence level. The IRAS data do not distinguish between Lagrangian and Eulerian local bias.

The effect of massive neutrinos on the matter power spectrum

We compute the bispectrum for the IRAS PSCz catalog and find that the galaxy distribution displays the characteristic signature of gravity. Assuming Gaussian initial conditions, we obtain galaxy biasing parameters 1/b(1) = 1.20(+0.18)(-0.19) and b(2)/b(2)(1) = -0.42+/-0.19, with no sign of scale-dependent bias for k < or = 0.3h Mpc(-1). These results impose stringent constraints on non-Gaussian initial conditions. For dimensional scaling models with chi(2)(N) statistics, we find N > 49, which implies a constraint on primordial skewness B3 < 0.35.