Cosmic microwave background anisotropy power spectrum statistics for high precision cosmology

As the era of high precision cosmology approaches, the empirically determined power spectrum of the microwave background anisotropy, $C_l$, will provide a crucial test for cosmological theories. We present a unified semi-analytic framework for the study of the statistical properties of the $C_l$ coefficients computed from the results of balloon, ground based, and satellite experiments. An illustrative application shows that commonly used approximations {\it bias} the estimation of the baryon parameter $\Omega_b$ at the 1% level even for a satellite capturing as much as $\sim 70$% of the sky.Comment: 4 pages, 3 figures. Also available at http://www.tac.dk/~wandelt/downloads.htm

Channeling in direct dark matter detection I: channeling fraction in NaI (Tl) crystals

The channeling of the ion recoiling after a collision with a WIMP changes the ionization signal in direct detection experiments, producing a larger signal than otherwise expected. We give estimates of the fraction of channeled recoiling ions in NaI (Tl) crystals using analytic models produced since the 1960's and 70's to describe channeling and blocking effects. We find that the channeling fraction of recoiling lattice nuclei is smaller than that of ions that are injected into the crystal and that it is strongly temperature dependent.Comment: 37 pages, 35 figures, Accepted for publication in JCAP on 27 October 2010, Minor revisions: added an appendix, updated references, updated Fig. 9, corrected a few typo

Using CMB data to constrain non-isotropic Planck-scale modifications to Electrodynamics

We develop a method to constrain non-isotropic features of Cosmic Microwave Background (CMB) polarization, of a type expected to arise in some models describing quantum gravity effects on light propagation. We describe the expected signatures of this kind of anomalous light propagation on CMB photons, showing that it will produce a non-isotropic birefringence effect, i.e. a rotation of the CMB polarization direction whose observed amount depends in a peculiar way on the observation direction. We also show that the sensitivity levels expected for CMB polarization studies by the \emph{Planck} satellite are sufficient for testing these effects if, as assumed in the quantum-gravity literature, their magnitude is set by the minute Planck length.Comment: 18 pages, 4 figures, 2 table

Probing Cosmic Strings with Satellite CMB measurements

We study the problem of searching for cosmic string signal patterns in the present high resolution and high sensitivity observations of the Cosmic Microwave Background (CMB). This article discusses a technique capable of recognizing Kaiser-Stebbins effect signatures in total intensity anisotropy maps, and shows that the biggest factor that produces confusion is represented by the acoustic oscillation features of the scale comparable to the size of horizon at recombination. Simulations show that the distribution of null signals for pure Gaussian maps converges to a $\chi^2$ distribution, with detectability threshold corresponding to a string induced step signal with an amplitude of about 100 \muK which corresponds to a limit of roughly $G\mu < 1.5\times 10^{-6}$. We study the statistics of spurious detections caused by extra-Galactic and Galactic foregrounds. For diffuse Galactic foregrounds, which represents the dominant source of contamination, we derive sky masks outlining the available region of the sky where the Galactic confusion is sub-dominant, specializing our analysis to the case represented by the frequency coverage and nominal sensitivity and resolution of the Planck experiment.Comment: 14 pages, 3 figures, to be published in JCA

Can we detect Hot or Cold spots in the CMB with Minkowski Functionals?

In this paper, we investigate the utility of Minkowski Functionals as a probe of cold/hot disk-like structures in the CMB. In order to construct an accurate estimator, we resolve a long-standing issue with the use of Minkowski Functionals as probes of the CMB sky -- namely that of systematic differences ("residuals") when numerical and analytical MF are compared. We show that such residuals are in fact by-products of binning, and not caused by pixelation or masking as originally thought. We then derive a map-independent estimator that encodes the effects of binning, applicable to beyond our present work. Using this residual-free estimator, we show that small disk-like effects (as claimed by Vielva et al.) can be detected only when a large sample of such maps are averaged over. In other words, our estimator is noise-dominated for small disk sizes at WMAP resolution. To confirm our suspicion, we apply our estimator to the WMAP7 data to obtain a null result.Comment: 15 pages, 13 figure

A small universe after all?

The cosmic microwave background radiation allows us to measure both the geometry and topology of the universe. It has been argued that the COBE-DMR data already rule out models that are multiply connected on scales smaller than the particle horizon. Here we show the opposite is true: compact (small) hyperbolic universes are favoured over their infinite counterparts. For a density parameter of Omega_o=0.3, the compact models are a better fit to COBE-DMR (relative likelihood ~20) and the large-scale structure data (sigma_8 increases by ~25%).Comment: 4 pages, RevTeX, 7 Figure

Analysis of CMB polarization on an incomplete sky

The full sky cosmic microwave background polarization field can be decomposed into 'electric' and 'magnetic' components. Working in harmonic space we construct window functions that allow clean separation of the electric and magnetic modes from observations over only a portion of the sky. Our construction is exact for azimuthally symmetric patches, but should continue to perform well for arbitrary patches. From the window functions we obtain variables that allow for robust estimation of the magnetic component without risk of contamination from the probably much larger electric signal. For isotropic, uncorrelated noise the variables have a very simple diagonal noise correlation, and further analysis using them should be no harder than analysing the temperature field. For an azimuthally-symmetric patch, such as that obtained from survey missions when the galactic region is removed, the exactly-separated variables are fast to compute allowing us to estimate the magnetic signal that could be detected by the Planck satellite in the absence of non-galactic foregrounds. We also discuss the sensitivity of future experiments to tensor modes in the presence of a magnetic signal generated by weak lensing, and give lossless methods for analysing the electric polarization field in the case that the magnetic component is negligible.Comment: 27 pages, 8 figures. New appendix on weak signal detection and revised plots using a better statistic. Other changes to match version accepted by PRD. Sample source code now available at http://cosmologist.info/pola

Relativistic positioning: four-dimensional numerical approach in Minkowski space-time

We simulate the satellite constellations of two Global Navigation Satellite Systems: Galileo (EU) and GPS (USA). Satellite motions are described in the Schwarzschild space-time produced by an idealized spherically symmetric non rotating Earth. The trajectories are then circumferences centered at the same point as Earth. Photon motions are described in Minkowski space-time, where there is a well known relation, Coll, Ferrando & Morales-Lladosa (2010), between the emission and inertial coordinates of any event. Here, this relation is implemented in a numerical code, which is tested and applied. The first application is a detailed numerical four-dimensional analysis of the so-called emission coordinate region and co-region. In a second application, a GPS (Galileo) satellite is considered as the receiver and its emission coordinates are given by four Galileo (GPS) satellites. The bifurcation problem (double localization) in the positioning of the receiver satellite is then pointed out and discussed in detail.Comment: 16 pages, 9 figures, published (online) in Astrophys. Space Sc

Temperature and Polarization Patterns in Anisotropic Cosmologies

We study the coherent temperature and polarization patterns produced in homogeneous but anisotropic cosmological models. We show results for all Bianchi types with a Friedman-Robertson-Walker limit (i.e. Types I, V, VII$_{0}$, VII$_{h}$ and IX) to illustrate the range of possible behaviour. We discuss the role of spatial curvature, shear and rotation in the geodesic equations for each model and establish some basic results concerning the symmetries of the patterns produced. We also give examples of the time-evolution of these patterns in terms of the Stokes parameters $I$, $Q$ and $U$.Comment: 24 pages, 7 Figures, submitted to JCAP. Revised version: numerous references added, text rewritten, and errors corrected

Constraining the Power Spectrum using Clusters

(Shortened Abstract). We analyze a redshift sample of Abell/ACO clusters and compare them with numerical simulations based on the truncated Zel'dovich approximation (TZA), for a list of eleven dark matter (DM) models. For each model we run several realizations, on which we estimate cosmic variance effects. We analyse correlation statistics, the probability density function, and supercluster properties from percolation analysis. As a general result, we find that the distribution of galaxy clusters provides a constraint only on the shape of the power spectrum, but not on its amplitude: a shape parameter 0.18 < \Gamma < 0.25 and an effective spectral index at 20Mpc/h in the range [-1.1,-0.9] are required by the Abell/ACO data. In order to obtain complementary constraints on the spectrum amplitude, we consider the cluster abundance as estimated using the Press--Schechter approach, whose reliability is explicitly tested against N--body simulations. We conclude that, of the cosmological models considered here, the only viable models are either Cold+Hot DM ones with \Omega_\nu = [0.2-0.3], better if shared between two massive neutrinos, and flat low-density CDM models with \Omega_0 = [0.3-0.5].Comment: 37 pages, Latex file, 9 figures; New Astronomy, in pres