Power Spectrum Estimators For Large CMB Datasets

Forthcoming high-resolution observations of the Cosmic Microwave Background (CMB) radiation will generate datasets many orders of magnitude larger than have been obtained to date. The size and complexity of such datasets presents a very serious challenge to analysing them with existing or anticipated computers. Here we present an investigation of the currently favored algorithm for obtaining the power spectrum from a sky-temperature map --- the quadratic estimator. We show that, whilst improving on direct evaluation of the likelihood function, current implementations still inherently scale as the equivalent of the cube of the number of pixels or worse, and demonstrate the critical importance of choosing the right implementation for a particular dataset.Comment: 8 pages LATEX, no figures, corrected misaligned columns in table

Cosmological predictions from the Misner brane

Within the spirit of five-dimensional gravity in the Randall-Sundrum scenario, in this paper we consider cosmological and gravitational implications induced by forcing the spacetime metric to satisfy a Misner-like symmetry. We first show that in the resulting Misner-brane framework the Friedmann metric for a radiation dominated flat universe and the Schwarzschild or anti-de Sitter black holes metrics are exact solutions on the branes, but the model cannot accommodate any inflationary solution. The horizon and flatness problems can however be solved in Misner-brane cosmology by causal and noncausal communications through the extra dimension between distant regions which are outside the horizon. Based on a semiclassical approximation to the path-integral approach, we have calculated the quantum state of the Misner-brane universe and the quantum perturbations induced on its metric by brane propagation along the fifth direction. We have then considered testable predictions from our model. These include a scale-invariant spectrum of density perturbations whose amplitude can be naturally accommodated to the required value 10$^{-5}-10^{-6}$, and a power spectrum of CMB anisotropies whose acoustic peaks are at the same sky angles as those predicted by inflationary models, but having much smaller secondary-peak intensities. These predictions seem to be compatible with COBE and recent Boomerang and Maxima measurementsComment: 16 pages, RevTe

Small mammals and habitat structure along altitudinal gradients in the southern Cape mountains

Small mammals were sampled along altitudinal gradients in two mountain localities, the Swartberg and Baviaanskloof, in the southern Cape in summer 1977–1978. Species composition varied according to altitude and aspect with a total catch of six rodent and two shrew species. Correlations were found between abundance of rodent species and habitat variables, particularly vegetation structure and the cover of rock and bare soil. Rodent species diversity was negatively correlated with the proportion of total foliage at low to mid heights (40 - 80 cm). Factors controlling apparent habitat preferences are discussed together with modes of rodent niche separation. Extrapolation of the results is limited by the single season and restricted geographical coverage of the survey

Fast, exact CMB power spectrum estimation for a certain class of observational strategies

We describe a class of observational strategies for probing the anisotropies in the cosmic microwave background (CMB) where the instrument scans on rings which can be combined into an n-torus, the {\em ring torus}. This class has the remarkable property that it allows exact maximum likelihood power spectrum estimation in of order $N^2$ operations (if the size of the data set is $N$) under circumstances which would previously have made this analysis intractable: correlated receiver noise, arbitrary asymmetric beam shapes and far side lobes, non-uniform distribution of integration time on the sky and partial sky coverage. This ease of computation gives us an important theoretical tool for understanding the impact of instrumental effects on CMB observables and hence for the design and analysis of the CMB observations of the future. There are members of this class which closely approximate the MAP and Planck satellite missions. We present a numerical example where we apply our ring torus methods to a simulated data set from a CMB mission covering a 20 degree patch on the sky to compute the maximum likelihood estimate of the power spectrum $C_\ell$ with unprecedented efficiency.Comment: RevTeX, 14 pages, 5 figures. A full resolution version of Figure 1 and additional materials are at http://feynman.princeton.edu/~bwandelt/RT

Computing CMB Anisotropy in Compact Hyperbolic Spaces

The measurements of CMB anisotropy have opened up a window for probing the global topology of the universe on length scales comparable to and beyond the Hubble radius. For compact topologies, the two main effects on the CMB are: (1) the breaking of statistical isotropy in characteristic patterns determined by the photon geodesic structure of the manifold and (2) an infrared cutoff in the power spectrum of perturbations imposed by the finite spatial extent. We present a completely general scheme using the regularized method of images for calculating CMB anisotropy in models with nontrivial topology, and apply it to the computationally challenging compact hyperbolic topologies. This new technique eliminates the need for the difficult task of spatial eigenmode decomposition on these spaces. We estimate a Bayesian probability for a selection of models by confronting the theoretical pixel-pixel temperature correlation function with the COBE-DMR data. Our results demonstrate that strong constraints on compactness arise: if the universe is small compared to the `horizon' size, correlations appear in the maps that are irreconcilable with the observations. If the universe is of comparable size, the likelihood function is very dependent upon orientation of the manifold wrt the sky. While most orientations may be strongly ruled out, it sometimes happens that for a specific orientation the predicted correlation patterns are preferred over the conventional infinite models.Comment: 15 pages, LaTeX (IOP style included), 3 color figures (GIF) in separate files. Minor revision to match the version accepted in Class. Quantum Grav.: Proc. of Topology and Cosmology, Cleveland, 1997. The paper can be also downloaded from http://www.cita.utoronto.ca/~pogosyan/cwru_proc.ps.g

CMBfit: Rapid WMAP likelihood calculations with normal parameters

We present a method for ultra-fast confrontation of the WMAP cosmic microwave background observations with theoretical models, implemented as a publicly available software package called CMBfit, useful for anyone wishing to measure cosmological parameters by combining WMAP with other observations. The method takes advantage of the underlying physics by transforming into a set of parameters where the WMAP likelihood surface is accurately fit by the exponential of a quartic or sextic polynomial. Building on previous physics based approximations by Hu et.al., Kosowsky et.al. and Chu et.al., it combines their speed with precision cosmology grade accuracy. A Fortran code for computing the WMAP likelihood for a given set of parameters is provided, pre-calibrated against CMBfast, accurate to Delta lnL ~ 0.05 over the entire 2sigma region of the parameter space for 6 parameter ``vanilla'' Lambda CDM models. We also provide 7-parameter fits including spatial curvature, gravitational waves and a running spectral index.Comment: 14 pages, 8 figures, References added, accepted for publication in Phys.Rev.D., a Fortran code can be downloaded from http://space.mit.edu/home/tegmark/cmbfit