Geometrical estimators as a test of Gaussianity in the CMB

We investigate the power of geometrical estimators on detecting non-Gaussianity in the cosmic microwave background. In particular the number, eccentricity and Gaussian curvature of excursion sets above (and below) a threshold are studied. We compare their different performance when applied to non-Gaussian simulated maps of small patches of the sky, which take into account the angular resolution and instrumental noise of the Planck satellite. These non-Gaussian simulations are obtained as perturbations of a Gaussian field in two different ways which introduce a small level of skewness or kurtosis in the distribution. A comparison with a classical estimator, the genus, is also shown. We find that the Gaussian curvature is the best of our estimators in all the considered cases. Therefore we propose the use of this quantity as a particularly useful test to look for non-Gaussianity in the CMB.Comment: 9 pages, 6 postscript figures, submitted to MNRA

Quasar-galaxy associations revisited

Gravitational lensing predicts an enhancement of the density of bright, distant QSOs around foreground galaxies. We measure this QSO-galaxy correlation w_qg for two complete samples of radio-loud quasars, the southern 1Jy and Half-Jansky samples. The existence of a positive correlation between z~1 quasars and z~0.15 galaxies is confirmed at a p=99.0% significance level (>99.9%) if previous measurements on the northern hemisphere are included). A comparison with the results obtained for incomplete quasar catalogs (e.g. the Veron-Cetty and Veron compilation) suggests the existence of an `identification bias', which spuriously increases the estimated amplitude of the quasar-galaxy correlation for incomplete samples. This effect may explain many of the surprisingly strong quasar-galaxy associations found in the literature. Nevertheless, the value of w_qg that we measure in our complete catalogs is still considerably higher than the predictions from weak lensing. We consider two effects which could help to explain this discrepancy: galactic dust extinction and strong lensing.Comment: 9 pages, 6 figures, MNRAS accepte

Constraining our Universe with X-ray & Optical Cluster Data

We have used recent X-ray and optical data in order to impose some constraints on the cosmology and cluster scaling relations. Generically two kind of hypotheses define our model. First we consider that the cluster population is well described by the standard Press-Schechter (PS) formalism, and second, these clusters are supposed to follow scaling relations with mass: Temperature-Mass (T-M) and X-ray Luminosity-Mass (L_x - M). As a difference with many other authors we do not assume specific scaling relations to model cluster properties such as the usual $T-M$ virial relation or one observational determination of the $L_x-T$ relation. Instead we consider general free parameter scaling relations. With the previous model (PS plus scalings) we fit our free parameters to several X-ray and optical data with the advantage over many other works that we consider all the data sets at the same time. This prevents us from being inconsistent with some of the available observations. Among other interesting conclusions, we find that only low-density universes are compatible with all the data considered and that the degeneracy between $\Omega_m$ and $\sigma_8$ is broken. Also we obtain interesting limits on the parameters characterizing the scaling relations.Comment: 11 pages, 7 figures. MNRAS accepted versio

Genus and spot density in the COBE DMR first year anisotropy maps

A statistical analysis of texture on the {\it COBE}-DMR first year sky maps based on the genus and spot number is presented. A generalized $\chi^2$ statistic is defined in terms of ``observable'' quantities: the genus and spot density that would be measured by different cosmic observers. This strategy together with the use of Monte Carlo simulations of the temperature fluctuations, including all the relevant experimental parameters, represent the main difference with previous analyses. Based on the genus analysis we find a strong anticorrelation between the quadrupole amplitude $Q_{rms-PS}$ and the spectral index $n$ of the density fluctuation power spectrum at recombination of the form $Q_{rms-PS}= 22.2 \pm 1.7 - (4.7 \pm 1.3) \times n\ \mu$K for fixed $n$, consistent with previous works. The result obtained based on the spot density is consistent with this $Q_{rms-PS} (n)$ relation. In addition to the previous results we have determined, using Monte Carlo simulations, the minimum uncertainty due to cosmic variance for the determination of the spectral index with the genus analysis. This uncertainty is $\delta n\approx 0.2$.Comment: 5 pages, uuencode file containing text and 1 figure. MNRAS in press