Efficient decomposition of cosmic microwave background polarization maps into pure E, pure B, and ambiguous components

Separation of the B component of a cosmic microwave background (CMB) polarization map from the much larger E component is an essential step in CMB polarimetry. For a map with incomplete sky coverage, this separation is necessarily hampered by the presence of "ambiguous" modes which could be either E or B modes. I present an efficient pixel-space algorithm for removing the ambiguous modes and separating the map into "pure" E and B components. The method, which works for arbitrary geometries, does not involve generating a complete basis of such modes and scales the cube of the number of pixels on the boundary of the map.Comment: Minor changes to previous version. Accepted for publication in Phys. Rev.

The COBE Normalization of CMB Anisotropies

With the advent of the COBE detection of fluctuations in the Cosmic Microwave Background radiation, the study of inhomogeneous cosmology has entered a new phase. It is now possible to accurately normalize fluctuations on the largest observable scales, in the linear regime. In this paper we present a model-independent method of normalizing theories to the full COBE data. This technique allows an extremely wide range of theories to be accurately normalized to COBE in a very simple and fast way. We give the best fitting normalization and relative peak likelihoods for a range of spectral shapes, and discuss the normalization for several popular theories. Additionally we present both Bayesian and frequentist measures of the goodness of fit of a representative range of theories to the COBE data.Comment: References updated, one figure redraw

The Meaning of Einstein's Equation

This is a brief introduction to general relativity, designed for both students and teachers of the subject. While there are many excellent expositions of general relativity, few adequately explain the geometrical meaning of the basic equation of the theory: Einstein's equation. Here we give a simple formulation of this equation in terms of the motion of freely falling test particles. We also sketch some of its consequences, and explain how the formulation given here is equivalent to the usual one in terms of tensors. Finally, we include an annotated bibliography of books, articles and websites suitable for the student of relativity.Comment: 23 pages LaTeX, 8 encapsulated Postscript figures; unlike the published version this includes a derivation of the inverse-square force la

Evolution and Earth's Entropy

Entropy decreases on the Earth due to day/night temperature differences. This decrease exceeds the decrease in entropy on the Earth related to evolution by many orders of magnitude. Claims by creationists that science is somehow inconsistent with regard to evolution are thus show to be baseless.Comment: 2 page

The COBE Normalization for Standard CDM

The COBE detection of CMB anisotropies provides the best way of fixing the amplitude of fluctuations on the largest scales. This normalization is usually given for an n=1 spectrum, including only the anisotropy caused by the Sachs- Wolfe effect. This is certainly not a good approximation for a model containing any reasonable amount of baryonic matter. In fact, even tilted S-W spectra are not a good fit to models like CDM. Here we normalize standard CDM (sCDM) to the 2-year COBE data, and quote the best amplitude in terms of the conventionally used measures of power. We also give normalizations for some specific variants of this standard model, and we indicate how the normalization depends on the assumed values of n, Omega_B and H_0. For sCDM we find =19.9\pm1.5uK, corresponding to sigma_8=1.34\pm0.10, with the normalization at large scales being B=(8.16\pm1.04)\times10^5 (Mpc/h)^4, and other numbers given in the Table. The measured rms temperature fluctuation smoothed on 10deg is a little low relative to this normalization. This is mainly due to the low quadrupole in the data: when the quadrupole is removed, the measured value of sigma(10) is quite consistent with the best-fitting . The use of should be preferred over sigma(10), when its value can be determined for a particular theory, since it makes full use of the data.Comment: 4 pages compressed uuencoded postscript. We have corrected an error in our analysi

The Wiener-Filtered COBE DMR Data and Predictions for the Tenerife Experiment

We apply a Wiener filter to the two-year COBE DMR data. The resulting sky map has significantly reduced noise levels compared to the raw data: the most prominent hot and cold spots are significant at the 4-sigma level. Furthermore, the entire covariance matrix of the errors in the filtered sky map is known, and it is therefore possible to make constrained realizations of the microwave sky with the correct a posteriori probability distribution. The filtered DMR sky map is used to make predictions for the Tenerife experiment. Two prominent features are predicted in a region of the sky not yet analyzed by the Tenerife group. The presence of these features is a robust prediction of the standard cosmological paradigm; if these features are not observed, some of our fundamental assumptions must be incorrect.Comment: 15 pages of uuencoded compressed PostScript. A PostScript file including figures is available at ftp://pac2.berkeley.edu/pub/bunn/wienerten