CMB Anisotropy in Compact Hyperbolic Universes I: Computing Correlation Functions

CMB anisotropy measurements have brought the issue of global topology of the universe from the realm of theoretical possibility to within the grasp of observations. The global topology of the universe modifies the correlation properties of cosmic fields. In particular, strong correlations are predicted in CMB anisotropy patterns on the largest observable scales if the size of the Universe is comparable to the distance to the CMB last scattering surface. We describe in detail our completely general scheme using a regularized method of images for calculating such correlation functions in models with nontrivial topology, and apply it to the computationally challenging compact hyperbolic spaces. Our procedure directly sums over images within a specified radius, ideally many times the diameter of the space, effectively treats more distant images in a continuous approximation, and uses Cesaro resummation to further sharpen the results. At all levels of approximation the symmetries of the space are preserved in the correlation function. This new technique eliminates the need for the difficult task of spatial eigenmode decomposition on these spaces. Although the eigenspectrum can be obtained by this method if desired, at a given level of approximation the correlation functions are more accurately determined. We use the 3-torus example to demonstrate that the method works very well. We apply it to power spectrum as well as correlation function evaluations in a number of compact hyperbolic (CH) spaces. Application to the computation of CMB anisotropy correlations on CH spaces, and the observational constraints following from them, are given in a companion paper.Comment: 27 pages, Latex, 11 figures, submitted to Phys. Rev. D, March 11, 199

CMB Anisotropy in Compact Hyperbolic Universes II: COBE Maps and Limits

We calculate the CMB anisotropy in compact hyperbolic universe models using the regularized method of images described in paper-I, including the 'line-of-sight `integrated Sachs-Wolfe' effect, as well as the last-scattering surface terms. We calculate the Bayesian probabilities for a selection of models by confronting our theoretical pixel-pixel temperature correlation functions with the COBE-DMR data. Our results demonstrate that strong constraints on compactness arise: if the universe is small compared to the `horizon' size, correlations appear in the maps that are irreconcilable with the observations. This conclusion is qualitatively insensitive to the matter content of the universe, in particular, the presence of a cosmological constant. If the universe is of comparable size to the 'horizon', the likelihood function is very dependent upon orientation of the manifold wrt the sky. While most orientations may be strongly ruled out, it sometimes happens that for a specific orientation the predicted correlation patterns are preferred over those for the conventional infinite models. The full Bayesian analysis we use is the most complete statistical test that can be done on the COBE maps, taking into account all possible signals and their variances in the theoretical skies, in particular the high degree of anisotropic correlation that can exist. We show that standard visual measures for comparing theoretical predictions with the data such as the isotropized power spectrum $C_\ell$ are not so useful in small compact spaces because of enhanced cosmic variance associated with the breakdown of statistical isotropy.Comment: 29 pages, Latex, 15 figures, submitted to Phys. Rev. D, March 11, 1999. Full resolution figures can be obtained from ftp://ftp.cita.utoronto.ca/pogosyan/prdB

Non-Gaussian Minkowski functionals & extrema counts in redshift space

In the context of upcoming large-scale structure surveys such as Euclid, it is of prime importance to quantify the effect of peculiar velocities on geometric probes. Hence the formalism to compute in redshift space the geometrical and topological one-point statistics of mildly non-Gaussian 2D and 3D cosmic fields is developed. Leveraging the partial isotropy of the target statistics, the Gram-Charlier expansion of the joint probability distribution of the field and its derivatives is reformulated in terms of the corresponding anisotropic variables. In particular, the cosmic non-linear evolution of the Minkowski functionals, together with the statistics of extrema are investigated in turn for 3D catalogues and 2D slabs. The amplitude of the non-Gaussian redshift distortion correction is estimated for these geometric probes. In 3D, gravitational perturbation theory is implemented in redshift space to predict the cosmic evolution of all relevant Gram-Charlier coefficients. Applications to the estimation of the cosmic parameters sigma(z) and beta=f/b1 from upcoming surveys is discussed. Such statistics are of interest for anisotropic fields beyond cosmology.Comment: 35 pages, 15 figures, matches version published in MNRAS with a typo corrected in eq A1

The Skeleton: Connecting Large Scale Structures to Galaxy Formation

We report on two quantitative, morphological estimators of the filamentary structure of the Cosmic Web, the so-called global and local skeletons. The first, based on a global study of the matter density gradient flow, allows us to study the connectivity between a density peak and its surroundings, with direct relevance to the anisotropic accretion via cold flows on galactic halos. From the second, based on a local constraint equation involving the derivatives of the field, we can derive predictions for powerful statistics, such as the differential length and the relative saddle to extrema counts of the Cosmic web as a function of density threshold (with application to percolation of structures and connectivity), as well as a theoretical framework to study their cosmic evolution through the onset of gravity-induced non-linearities.Comment: 10 pages, 8 figures; proceedings of the "Invisible Universe" 200

Intrinsic alignment of simulated galaxies in the cosmic web: implications for weak lensing surveys

The intrinsic alignment of galaxy shapes (by means of their angular momentum) and their cross-correlation with the surrounding dark matter tidal field are investigated using the 160 000, z=1.2 synthetic galaxies extracted from the high-resolution cosmological hydrodynamical simulation Horizon-AGN. One- and two-point statistics of the spin of the stellar component are measured as a function of mass and colour. For the low-mass galaxies, this spin is locally aligned with the tidal field `filamentary' direction while, for the high-mass galaxies, it is perpendicular to both filaments and walls. The bluest galaxies of our synthetic catalog are more strongly correlated with the surrounding tidal field than the reddest galaxies, and this correlation extends up to 10 Mpc/h comoving distance. We also report a correlation of the projected ellipticities of blue, intermediate mass galaxies on a similar scale at a level of 10^(-4) which could be a concern for cosmic shear measurements. We do not report any measurable intrinsic alignments of the reddest galaxies of our sample. This work is a first step toward the use of very realistic catalog of synthetic galaxies to evaluate the contamination of weak lensing measurement by the intrinsic galactic alignments.Comment: 15 pages, accepted for publication in MNRA

Cosmic microwave background snapshots: pre-WMAP and post-WMAP

Abbreviated: We highlight the remarkable evolution in the CMB power spectrum over the past few years, and in the cosmological parameters for minimal inflation models derived from it. Grand unified spectra (GUS) show pre-WMAP optimal bandpowers are in good agreement with each other and with the one-year WMAP results, which now dominate the L < 600 bands. GUS are used to determine calibrations, peak/dip locations and heights, and damping parameters. These CMB experiments significantly increased the case for accelerated expansion in the early universe (the inflationary paradigm) and at the current epoch (dark energy dominance) when they were combined with `prior' probabilities on the parameters. A minimal inflation parameter set is applied in the same way to the evolving data. Grid-based and and Monte Carlo Markov Chain methods are shown to give similar values, highly stable over time and for different prior choices, with the increasing precision best characterized by decreasing errors on uncorrelated parameter eigenmodes. After marginalizing over the other cosmic and experimental variables for a weak+LSS prior, the pre-WMAP data of Jan03 cf. the post-WMAP data of Mar03 give Omega_{tot} =1.03^{+0.05}_{-0.04} cf. 1.02^{+0.04}_{-0.03}. Adding the flat prior, n_s =0.95^{+0.07}_{-0.04} cf. 0.97^{+0.02}_{-0.02}, with < 2\sigma evidence for a log variation of n_s. The densities have concordance values. The dark energy pressure-to-density ratio is not well constrained by our weak+LSS prior, but adding SN1 gives w_Q < -0.7. We find \sigma_8 = 0.89^{+0.06}_{-0.07} cf. 0.86^{+0.04}_{-0.04}, implying a sizable SZ effect; the high L power suggest \sigma_8 \sim 0.94^{+0.08}_{-0.16} is needed to be SZ-compatible.Comment: 36 pages, 5 figures, 5 tables, Jan 2003 Roy Soc Discussion Meeting on `The search for dark matter and dark energy in the Universe', published PDF (Oct 15 2003) is http://www.cita.utoronto.ca/~bond/roysoc03/03TA2435.pd

QUANTITATIVE DETERMINATION OF PHENOL CARBOXYLIC ACIDS IN POMEGRANATE FRUIT PULP BY THE HIGH-PERFORMANCE LIQUID CHROMATOGRAPHY WITH ULTRAVIOLET DETECTION

Objective: Pomegranate (Punica granatum L.) is a broadly used plant possessing a wide range of medicinal properties. In this research, we have mainly focused on the investigation of phenolic compounds of pomegranate fruit pulp (PFP).Methods: Fresh fruits of Çəhrayı Gülöyşə,†Kizil-anor,†and pomegranate varietal mixture were used as samples. High-performance liquid chromatography-ultraviolet (HPLC-UV) analysis of phenol carboxylic acids was performed with metal column Kromasil® C18 (4.6×250 mm, particle size 5 μm) and the acetonitrile-water-concentrated acid phosphoric system (400:600:5) under isocratic elution conditions (flow rate of 0.5 ml/min). Detection was carried out using a UV detector GILSTON†UV/Visible model 151 at a wavelength of 280 nm.Results and Discussion: As a result of our research, we proposed chromatographic conditions for the separation of phenolic compounds, the conditions for sample preparation of PFP. Procedure for determination of phenolic carboxylic acids total content in terms of gallic acid by HPLC-UV method was developed. According to the obtained data, the content of phenolic carboxylic acids should be at least 0.7%.Conclusion: Procedure for the quantitative determination of gallic acid using the HPLC-UV method was developed. This method which can be used in the standardization of new medicinal plant raw materials - PFP, as well as extract preparations based on it in the future