Constrained probability distributions of correlation functions

Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation. However, this has been shown to be insufficient. Aims: For the case of Gaussian random fields, we search for an exact probability distribution of correlation functions, which could improve the accuracy of future data analyses. Methods: We use a fully analytic approach, first expanding the random field in its Fourier modes, and then calculating the characteristic function. Finally, we derive the probability distribution function using integration by residues. We use a numerical implementation of the full analytic formula to discuss the behaviour of this function. Results: We derive the univariate and bivariate probability distribution function of the correlation functions of a Gaussian random field, and outline how higher joint distributions could be calculated. We give the results in the form of mode expansions, but in one special case we also find a closed-form expression. We calculate the moments of the distribution and, in the univariate case, we discuss the Edgeworth expansion approximation. We also comment on the difficulties in a fast and exact numerical implementation of our results, and on possible future applications.Comment: 13 pages, 5 figures, updated to match version published in A&A (slightly expanded Sects. 5.3 and 6

Power Spectra in Global Defect Theories of Cosmic Structure Formation

An efficient technique for computing perturbation power spectra in field ordering theories of cosmic structure formation is introduced, enabling computations to be carried out with unprecedented precision. Large scale simulations are used to measure unequal time correlators of the source stress energy, taking advantage of scaling during matter and radiation domination, and causality, to make optimal use of the available dynamic range. The correlators are then re-expressed in terms of a sum of eigenvector products, a representation which we argue is optimal, enabling the computation of the final power spectra to be performed at high accuracy. Microwave anisotropy and matter perturbation power spectra for global strings, monopoles, textures and non-topological textures are presented and compared with recent observations.Comment: 4 pages, compressed and uuencoded RevTex file and postscript figure

Polarization of the Microwave Background in Defect Models

We compute the polarization power spectra for global strings, monopoles, textures and nontopological textures, and compare them to inflationary models. We find that topological defect models predict a significant (1 microK) contribution to magnetic type polarization on degree angular scales, which is produced by the large vector component of the defect source. We also investigate the effect of decoherence on polarization. It leads to a smoothing of acoustic oscillations both in temperature and polarization power spectra and strongly suppresses the cross-correlation between temperature and polarization relative to inflationary models. Presence or absence of magnetic polarization or cross-correlation would be a strong discriminator between the two theories of structure formation and will be testable with the next generation of CMB satellites.Comment: 4 pages, 3 figures, RevTeX fil

Standard and non-standard primordial neutrinos

The standard cosmological model predicts the existence of a cosmic neutrino background with a present density of about 110 cm^{-3} per flavour, which affects big-bang nucleosynthesis, cosmic microwave background anisotropies, and the evolution of large scale structures. We report on a precision calculation of the cosmic neutrino background properties including the modification introduced by neutrino oscillations. The role of a possible neutrino-antineutrino asymmetry and the impact of non-standard neutrino-electron interactions on the relic neutrinos are also briefly discussed.Comment: 4 pages, no figures. Contribution to the proceedings of SNOW 2006, Stockholm, May 2-6, 2006. Typos corrected, updated reference

Direct Signature of Evolving Gravitational Potential from Cosmic Microwave Background

We show that time dependent gravitational potential can be directly detected from the cosmic microwave background (CMB) anisotropies. The signature can be measured by cross-correlating the CMB with the projected density field reconstructed from the weak lensing distortions of the CMB itself. The cross-correlation gives a signal whenever there is a time dependent gravitational potential. This method traces dark matter directly and has a well defined redshift distribution of the window projecting over the density perturbations, thereby avoiding the problems plaguing other proposed cross-correlations. We show that both MAP and Planck will be able to probe this effect for observationally relevant curvature and cosmological constant models, which will provide additional constraints on the cosmological parameters.Comment: 4 pages, 2 figures. Submitted to PR

Lensing of the CMB: Non Gaussian aspects

We study the generation of CMB anisotropies by gravitational lensing on small angular scales. We show these fluctuations are not Gaussian. We prove that the power spectrum of the tail of the CMB anisotropies on small angular scales directly gives the power spectrum of the deflection angle. We show that the generated power on small scales is correlated with the large scale gradient. The cross correlation between large scale gradient and small scale power can be used to test the hypothesis that the extra power is indeed generated by lensing. We compute the three and four point function of the temperature in the small angle limit. We relate the non-Gaussian aspects presented in this paper as well as those in our previous studies of the lensing effects on large scales to the three and four point functions. We interpret the statistics proposed in terms of different configurations of the four point function and show how they relate to the statistic that maximizes the S/N.Comment: Changes to match accepted version in PRD, 20 pages 10 figures. Better resolution images of the figures can be found at http://www.sns.ias.edu/~matiasz/RESEARCH/cmblensing.htm

Detecting the Earliest Galaxies Through Two New Sources of 21cm Fluctuations

The first galaxies that formed at a redshift ~20-30 emitted continuum photons with energies between the Lyman-alpha and Lyman limit wavelengths of hydrogen, to which the neutral universe was transparent except at the Lyman-series resonances. As these photons redshifted or scattered into the Lyman-alpha resonance they coupled the spin temperature of the 21cm transition of hydrogen to the gas temperature, allowing it to deviate from the microwave background temperature. We show that the fluctuations in the radiation emitted by the first galaxies produced strong fluctuations in the 21cm flux before the Lyman-alpha coupling became saturated. The fluctuations were caused by biased inhomogeneities in the density of galaxies, along with Poisson fluctuations in the number of galaxies. Observing the power-spectra of these two sources would probe the number density of the earliest galaxies and the typical mass of their host dark matter halos. The enhanced amplitude of the 21cm fluctuations from the era of Lyman-alpha coupling improves considerably the practical prospects for their detection.Comment: 11 pages, 7 figures, ApJ, published. Normalization fixed in top panels of Figures 4-

Weak Lensing of the CMB: A Harmonic Approach

Weak lensing of CMB anisotropies and polarization for the power spectra and higher order statistics can be handled directly in harmonic-space without recourse to real-space correlation functions. For the power spectra, this approach not only simplifies the calculations but is also readily generalized from the usual flat-sky approximation to the exact all-sky form by replacing Fourier harmonics with spherical harmonics. Counterintuitively, due to the nonlinear nature of the effect, errors in the flat-sky approximation do not improve on smaller scales. They remain at the 10% level through the acoustic regime and are sufficiently large to merit adoption of the all-sky formalism. For the bispectra, a cosmic variance limited detection of the correlation with secondary anisotropies has an order of magnitude greater signal-to-noise for combinations involving magnetic parity polarization than those involving the temperature alone. Detection of these bispectra will however be severely noise and foreground limited even with the Planck satellite, leaving room for improvement with higher sensitivity experiments. We also provide a general study of the correspondence between flat and all sky potentials, deflection angles, convergence and shear for the power spectra and bispectra.Comment: 17 pages, 5 figures, submitted to PR

Evidence for Quadratic Tidal Tensor Bias from the Halo Bispectrum

The relation between the clustering properties of luminous matter in the form of galaxies and the underlying dark matter distribution is of fundamental importance for the interpretation of ongoing and upcoming galaxy surveys. The so called local bias model, where galaxy density is a function of local matter density, is frequently discussed as a means to infer the matter power spectrum or correlation function from the measured galaxy correlation. However, gravitational evolution generates a term quadratic in the tidal tensor and thus non-local in the density field, even if this term is absent in the initial conditions (Lagrangian space). Because the term is quadratic, it contributes as a loop correction to the power spectrum, so the standard linear bias picture still applies on large scales, however, it contributes at leading order to the bispectrum for which it is significant on all scales. Such a term could also be present in Lagrangian space if halo formation were influenced by the tidal field. We measure the corresponding coupling strengths from the matter-matter-halo bispectrum in numerical simulations and find a non-vanishing coefficient for the tidal tensor term. We find no scale dependence of the bias parameters up to k=0.1 h/Mpc and that the tidal effect is increasing with halo mass. While the Lagrangian bias picture is a better description of our results than the Eulerian bias picture, our results suggest that there might be a tidal tensor bias already in the initial conditions. We also find that the coefficients of the quadratic density term deviate quite strongly from the theoretical predictions based on the spherical collapse model and a universal mass function. Both quadratic density and tidal tensor bias terms must be included in the modeling of galaxy clustering of current and future surveys if one wants to achieve the high precision cosmology promise of these datasets.Comment: 14 pages, 4 figures, 1 tabl