The Correlation Function of Clusters of Galaxies and the Amplitude of Mass Fluctuations in the Universe

We show that if a sample of galaxy clusters is complete above some mass threshold, then hierarchical clustering theories for structure formation predict its autocorrelation function to be determined purely by the cluster abundance and by the spectrum of linear density fluctuations. Thus if the shape of the initial fluctuation spectrum is known, its amplitude $\sigma_8$ can be estimated directly from the correlation length of a cluster sample in a way which is independent of the value of $\Omega_0$. If the cluster mass corresponding to the sample threshold is also known, it provides an independent estimate of the quantity $\sigma_8\Omega_0^{0.6}$. Thus cluster data should allow both $\sigma_8$ and $\Omega_0$ to be determined observationally. We explore these questions using N-body simulations together with a simple but accurate analytical model based on extensions of Press-Schechter theory. Applying our results to currently available data we find that if the linear fluctuation spectrum has a shape similar to that suggested by the APM galaxy survey, then a correlation length $r_0$ in excess of 20\mpch for Abell clusters would require $\sigma_8>1$, while r_0<15\mpch would require $\sigma_8<0.5$. With conventional estimates of the relevant mass threshold these imply \Omega_0\la 0.3 and \Omega_0\ga 1 respectively.Comment: Latex, 25 pages (including 8 PS figures). The PS-file of the paper is also available via anonymous ftp at: ftp://ibm-3.mpa-garching.mpg.de/pub/jing/xicc.ps . Submitted to MNRAS. In the replaced version, a typo in Eq.(1a) is fixe

QUASARS AND LARGE SCALE STRUCTURE OF THE UNIVERSE

The majority of bright distant quasars $(z {}^{>}_{\sim} 1)$ may form in massive mergers appearing in compact galaxy groups in/and young clusters. The expected tests are (i) large correlation signal for medium-$z$ QSOs $(1 < z < 2)$ and (ii) direct search for quasar groups (QGs) indicating positions of distant pre-superclusters which later will evolve to the "systems" like the local Great Attractor or Shapley concentration. We discuss large QGs with more than ten members within regions $\le l_{LS} \sim 100-150 \, h^{-1} Mpc$, tracing the enhanced density regions at $z {}^{<}_{\sim} 2$. These early large scale structures (i) provide a natural way to "bias" the distribution of Abell clusters, and (ii) suggest that the spectrum of primordial density perturbations is nearly flat at scales encompassing both cluster and GAs, $l = \pi k^{-1} \in(10,100)h^{-1} Mpc: \Delta^{2}_{k} \sim k^{3}P(k) \sim k^{\gamma}, \gamma = 1^{+0.6}_{-0.4}$.Comment: 5 pages, uuencoded Z-compressed postscript, contribution to the Proceedings of Rencontres de Moriond 1995 "Clustering in the Universe

Three-Point Correlations in Weak Lensing Surveys: Model Predictions and Applications

We use the halo model of clustering to compute two- and three-point correlation functions for weak lensing, and apply them in a new statistical technique to measure properties of massive halos. We present analytical results on the eight shear three-point correlation functions constructed using combination of the two shear components at each vertex of a triangle. We compare the amplitude and configuration dependence of the functions with ray-tracing simulations and find excellent agreement for different scales and models. These results are promising, since shear statistics are easier to measure than the convergence. In addition, the symmetry properties of the shear three-point functions provide a new and precise way of disentangling the lensing E-mode from the B-mode due to possible systematic errors. We develop an approach based on correlation functions to measure the properties of galaxy-group and cluster halos from lensing surveys. Shear correlations on small scales arise from the lensing matter within halos of mass M > 10^13 solar masses. Thus the measurement of two- and three-point correlations can be used to extract information on halo density profiles, primarily the inner slope and halo concentration. We demonstrate the feasibility of such an analysis for forthcoming surveys. We include covariances in the correlation functions due to sample variance and intrinsic ellipticity noise to show that 10% accuracy on profile parameters is achievable with surveys like the CFHT Legacy survey, and significantly better with future surveys. Our statistical approach is complementary to the standard approach of identifying individual objects in survey data and measuring their properties.Comment: 30 pages, 21 figures. Corrected typos in equations (23) and (28). Matches version for publication in MNRA

Primordial non-Gaussianity in the Bispectrum of the Halo Density Field

The bispectrum vanishes for linear Gaussian fields and is thus a sensitive probe of non-linearities and non-Gaussianities in the cosmic density field. Hence, a detection of the bispectrum in the halo density field would enable tight constraints on non-Gaussian processes in the early Universe and allow inference of the dynamics driving inflation. We present a tree level derivation of the halo bispectrum arising from non-linear clustering, non-linear biasing and primordial non-Gaussianity. A diagrammatic description is developed to provide an intuitive understanding of the contributing terms and their dependence on scale, shape and the non-Gaussianity parameter fNL. We compute the terms based on a multivariate bias expansion and the peak-background split method and show that non-Gaussian modifications to the bias parameters lead to amplifications of the tree level bispectrum that were ignored in previous studies. Our results are in a good agreement with published simulation measurements of the halo bispectrum. Finally, we estimate the expected signal to noise on fNL and show that the constraint obtainable from the bispectrum analysis significantly exceeds the one obtainable from the power spectrum analysis.Comment: 34 pages, 15 figures, (v3): matches JCAP published versio

Relativistic effects and primordial non-Gaussianity in the galaxy bias

When dealing with observables, one needs to generalize the bias relation between the observed galaxy fluctuation field to the underlying matter distribution in a gauge-invariant way. We provide such relation at second-order in perturbation theory adopting the local Eulerian bias model and starting from the observationally motivated uniform-redshift gauge. Our computation includes the presence of primordial non-Gaussianity. We show that large scale-dependent relativistic effects in the Eulerian bias arise independently from the presence of some primordial non-Gaussianity. Furthermore, the Eulerian bias inherits from the primordial non-Gaussianity not only a scale-dependence, but also a modulation with the angle of observation when sources with different biases are correlated.Comment: 12 pages, LaTeX file; version accepted for publication in JCA

Order parameter model for unstable multilane traffic flow

We discuss a phenomenological approach to the description of unstable vehicle motion on multilane highways that explains in a simple way the observed sequence of the phase transitions "free flow -> synchronized motion -> jam" as well as the hysteresis in the transition "free flow synchronized motion". We introduce a new variable called order parameter that accounts for possible correlations in the vehicle motion at different lanes. So, it is principally due to the "many-body" effects in the car interaction, which enables us to regard it as an additional independent state variable of traffic flow. Basing on the latest experimental data (cond-mat/9905216) we assume that these correlations are due to a small group of "fast" drivers. Taking into account the general properties of the driver behavior we write the governing equation for the order parameter. In this context we analyze the instability of homogeneous traffic flow manifesting itself in both of the mentioned above phase transitions where, in addition, the transition "synchronized motion -> jam" also exhibits a similar hysteresis. Besides, the jam is characterized by the vehicle flows at different lanes being independent of one another. We specify a certain simplified model in order to study the general features of the car cluster self-formation under the phase transition "free flow synchronized motion". In particular, we show that the main local parameters of the developed cluster are determined by the state characteristics of vehicle motion only.Comment: REVTeX 3.1, 10 pages with 10 PostScript figure

Constraining Primordial Non-Gaussianity with High-Redshift Probes

We present an analysis of the constraints on the amplitude of primordial non-Gaussianity of local type described by the dimensionless parameter $f_{\rm NL}$. These constraints are set by the auto-correlation functions (ACFs) of two large scale structure probes, the radio sources from NRAO VLA Sky Survey (NVSS) and the quasar catalogue of Sloan Digital Sky Survey Release Six (SDSS DR6 QSOs), as well as by their cross-correlation functions (CCFs) with the cosmic microwave background (CMB) temperature map (Integrated Sachs-Wolfe effect). Several systematic effects that may affect the observational estimates of the ACFs and of the CCFs are investigated and conservatively accounted for. Our approach exploits the large-scale scale-dependence of the non-Gaussian halo bias. The derived constraints on {$f_{\rm NL}$} coming from the NVSS CCF and from the QSO ACF and CCF are weaker than those previously obtained from the NVSS ACF, but still consistent with them. Finally, we obtain the constraints on $f_{\rm NL}=53\pm25$ ($1\,\sigma$) and $f_{\rm NL}=58\pm24$ ($1\,\sigma$) from NVSS data and SDSS DR6 QSO data, respectively.Comment: 16 pages, 8 figures, 1 table, Accepted for publication on JCA

CMBR Weak Lensing and HI 21-cm Cross-correlation Angular Power Spectrum

Weak gravitational lensing of the CMBR manifests as a secondary anisotropy in the temperature maps. The effect, quantified through the shear and convergence fields imprint the underlying large scale structure (LSS), geometry and evolution history of the Universe. It is hence perceived to be an important observational probe of cosmology. De-lensing the CMBR temperature maps is also crucial for detecting the gravitational wave generated B-modes. Future observations of redshifted 21-cm radiation from the cosmological neutral hydrogen (HI) distribution hold the potential of probing the LSS over a large redshift range. We have investigated the correlation between post-reionization HI signal and weak lensing convergence field. Assuming that the HI follows the dark matter distribution, the cross-correlation angular power spectrum at a multipole \ell is found to be proportional to the cold dark matter power spectrum evaluated at \ell/r, where r denotes the comoving distance to the redshift where the HI is located. The amplitude of the ross-correlation depends on quantities specific to the HI distribution, growth of perturbations and also the underlying cosmological model. In an ideal ituation, we found that a statistically significant detection of the cross-correlation signal is possible. If detected, the cross-correlation signal hold the possibility of a joint estimation of cosmological parameters and also test various CMBR de-lensing estimators.Comment: 14 pages, 4 figures, publishe

Consistency test of general relativity from large scale structure of the Universe

We construct a consistency test of General Relativity (GR) on cosmological scales. This test enables us to distinguish between the two alternatives to explain the late-time accelerated expansion of the universe, that is, dark energy models based on GR and modified gravity models without dark energy. We derive the consistency relation in GR which is written only in terms of observables - the Hubble parameter, the density perturbations, the peculiar velocities and the lensing potential. The breakdown of this consistency relation implies that the Newton constant which governs large-scale structure is different from that in the background cosmology, which is a typical feature in modified gravity models. We propose a method to perform this test by reconstructing the weak lensing spectrum from measured density perturbations and peculiar velocities. This reconstruction relies on Poisson's equation in GR to convert the density perturbations to the lensing potential. Hence any inconsistency between the reconstructed lensing spectrum and the measured lensing spectrum indicates the failure of GR on cosmological scales. The difficulties in performing this test using actual observations are discussed.Comment: 7 pages, 1 figur

Multiple sources of infection and potential endemic characteristics of the large outbreak of dengue in Guangdong in 2014

A large outbreak of dengue, with the most documented cases, occurred in Guangdong China in 2014. Epidemiological studies and phylogenetic analysis of the isolated dengue virus (DENV) showed this outbreak was attributed to multiple sources and caused by at least two genotypes of DENV-1 (Genotypes I and III) and two genotypes of DENV-2 (Cosmopolitan and Asian I Genotypes). A retrospective review and phylogenetic analysis of DENV isolated in Guangdong showed that DENV-1 Genotype I strains were reported continuously during 2004-2014, Genotype III strains were reported during 2009-2014 ; DENV-2 Cosmopolitan and Asian I Genotype strains were reported continuously during 2012-2014. At least 45,171 cases were reported in this outbreak, with 65.9% of the patients in the 21-55-year-old group. A trend toward a decrease in the daily newly emerged cases lagged by approximately 20 days compared with the mosquito density curve. Several epidemiological characteristics of this outbreak and the stably sustained serotypes and genotypes of DENV isolated in Guangdong suggest that Guangdong has been facing a threat of transforming from a dengue epidemic area to an endemic area. The high temperature, drenching rain, rapid urbanization, and pandemic of dengue in Southeast Asia may have contributed to this large outbreak of dengue