arXiv subjects

P. G. Castro

Publications and source records attributed to P. G. Castro.

25 records · Page 2Linked to original sources

arXiv2005

Weak lensing analysis in three dimensions

We present a comprehensive full-sky 3-dimensional analysis of the weak-lensing fields and their corresponding power spectra. Using the formalism of spin-weight spherical harmonics and spherical Bessel functions, we relate the two-point statistics of the harmonic expansion coefficients of the weak lensing shear and convergence to the power spectrum of the matter density perturbations, and derive small-angle limits. Such a study is relevant in view of the next generation of large-scale weak lensing surveys which will provide distance information about the sources through photometric redshifts. This opens up the possibility of accurate cosmological parameter estimation via weak lensing, with an emphasis on the equation of state of dark energy.

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arXiv2005

CMB temperature and polarisation pseudo-Cl estimators and covariances

We develop the pseudo-Cl method for reconstructing the Cosmic Microwave Background (CMB) temperature and polarization auto- and cross-power spectra, and estimate the pseudo-Cl covariance matrix for a realistic experiment on the cut sky. We calculate the full coupling equations for all six possible CMB power spectra, relating the observed pseudo-Cl's to the underlying all-sky Cl's, and test the reconstruction on both full-sky and cut-sky simulated CMB data sets. In particular we consider the reconstruction of the Cl from upcoming ground-based polarization experiments covering areas of a few hundred sq. degrees and find that the method is fast, unbiased and performs well over a wide range of multipoles from l=2 to l=2500. We then calculate the full covariance matrix between the modes of the pseudo-temperature and polarization power spectra, assuming that the underlying CMB fields are Gaussian randomly distributed. The complexity of the covariance matrix prohibits its rapid calculation, required for parameter estimation. Hence we present an approximation for the covariance matrix in terms of convolutions of the underlying power spectra. The coupling matrices in these expressions can be estimated by fitting to numerical simulations, circumventing direct and slow calculation, and further, inaccurate analytic approximations. We show that these coupling matrices are mostly independent of cosmology, and that the full covariance matrix for all six pseudo-Cl power spectra can be quickly and accurately calculated for any given cosmological model using this method. We compare these semi-analytic covariance matrices against simulations and find good agreement, the accuracy of which depends mainly on survey area and the range of cosmological parameters considered.

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arXiv2004

The Bispectrum and the Trispectrum of the Ostriker and Vishniac Effect

We present analytical expressions for the Fourier analog of the CMB three-point and four-point correlation functions, the spatial bispectrum and trispectrum, of the Ostriker and Vishniac effect in the linear and mildly nonlinear regime. Through this systematic study, we illustrate a technique to tackle the calculation of such statistics making use of the effects of its small-angle and vector-like properties through the Limber approximation. Finally we discuss its configuration dependence and detectability in the context of Gaussian theories for the currently favored flat Lambda CDM cosmology.

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arXiv2003

Non-Gaussianity: Comparing wavelet and Fourier based methods

In the context of the present and future Cosmic Microwave Background (CMB) experiments, going beyond the information provided by the power spectrum has become necessary in order to tightly constrain the cosmological model. The non-Gaussian signatures in the CMB represent a very promising tool to probe the early universe and the structure formation epoch. We present the results of a comparison between two families of non-Gaussian estimators: The first act on the wavelet space (skewness and excess kurtosis of the wavelet coefficients) and the second group on the Fourier space (bi- and trispectrum). We compare the relative sensitivities of these estimators by applying them to three different data sets meant to reproduce the majority of possible non-Gaussian contributions to the CMB. We find that the skewness in the wavelet space is slightly more sensitive than the bispectrum. For the four point estimators, we find that the excess kurtosis of the wavelet coefficients has very similar capabilities than the diagonal trispectrum while a near-diagonal trispectrum seems to be less sensitive to non-Gaussian signatures.

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arXiv2002

Cosmic Microwave Background anisotropies beyond the third peak

Forthcoming CMB experiments will allow us to accurately investigate the power spectrum at very small scales ($\ell > 1000$). We predict the level of the primary anisotropies, given the actual CMB measurements. The secondary anisotropies generated after matter-radiation decoupling contribute additional power in the tail of the CMB power spectrum. Together with the primary anisotropies, we compute the predicted power spectra for three dominant secondary effects induced by photon scattering. We predict these secondary contributions in flat cosmological models for parameters in agreement (to $2σ$) with the values allowed by current parameter estimates.

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arXiv2002

The Trispectrum of the 4 Year COBE-DMR data

We propose an estimator for the trispectrum of a scalar random field on a sphere, discuss its geometrical and statistical properties, and outline its implementation. By estimating the trispectrum of the 4 year COBE-DMR data (in HEALPix pixelization) we find new evidence of a non-Gaussian signal associated with a known systematic effect. We find that by removing data from the sky maps for those periods of time perturbed by this effect, the amplitudes of the trispectrum coefficients become completely consistent with predictions for a Gaussian sky. These results reinforce the importance of statistical methods based in harmonic space for quantifying non-Gaussianity.

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arXiv1998

Measurements of Omega and Lambda from 42 High-Redshift Supernovae

We report measurements of the mass density, Omega_M, and cosmological-constant energy density, Omega_Lambda, of the universe based on the analysis of 42 Type Ia supernovae discovered by the Supernova Cosmology Project. The magnitude-redshift data for these SNe, at redshifts between 0.18 and 0.83, are fit jointly with a set of SNe from the Calan/Tololo Supernova Survey, at redshifts below 0.1, to yield values for the cosmological parameters. All SN peak magnitudes are standardized using a SN Ia lightcurve width-luminosity relation. The measurement yields a joint probability distribution of the cosmological parameters that is approximated by the relation 0.8 Omega_M - 0.6 Omega_Lambda ~= -0.2 +/- 0.1 in the region of interest (Omega_M <~ 1.5). For a flat (Omega_M + Omega_Lambda = 1) cosmology we find Omega_M = 0.28{+0.09,-0.08} (1 sigma statistical) {+0.05,-0.04} (identified systematics). The data are strongly inconsistent with a Lambda = 0 flat cosmology, the simplest inflationary universe model. An open, Lambda = 0 cosmology also does not fit the data well: the data indicate that the cosmological constant is non-zero and positive, with a confidence of P(Lambda > 0) = 99%, including the identified systematic uncertainties. The best-fit age of the universe relative to the Hubble time is t_0 = 14.9{+1.4,-1.1} (0.63/h) Gyr for a flat cosmology. The size of our sample allows us to perform a variety of statistical tests to check for possible systematic errors and biases. We find no significant differences in either the host reddening distribution or Malmquist bias between the low-redshift Calan/Tololo sample and our high-redshift sample. The conclusions are robust whether or not a width-luminosity relation is used to standardize the SN peak magnitudes.

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