23 July 2002

6 August 2002

10 September 2002

Arthur Kosowsky

Efficient Estimation of the Microwave Background Power Spectrum  

I will describe highly accurate and efficient approximations for computing microwave background power spectra, using a physically motivated choice of variables. This technique can be used to simplify the task of constraining cosmological parameters from a measured power spectrum the case of the MAP satellite will be illustrated. Other applications and related technical issues may be discussed as well.

Matias Zaldarriaga

E/B Decomposition of Finite Pixelized CMB Maps  

Separation of the E and B components of a microwave background polarization map or weak lensing map is an essential step in extracting science from it, but when the map covers only part of the sky and/or is pixelized, this decomposition cannot be done perfectly. We present a method for decomposing an arbitrary sky map into a sum of three orthogonal components that we term "pure E", "pure B" and "ambiguous". This method is useful both for providing intuition for experimental design and for analyzing data sets in practice. We show how to find orthonormal bases for all three components in terms of bilaplacian eigenfunctions. The number of ambiguous modes is proportional to the length of the map boundary so fairly round maps are preferred. For real-world data analysis, we present a simple matrix eigenvalue method for calculating nearly pure E and B modes in pixelized maps. We find that the dominant source of leakage between E and B is aliasing of small-scale power caused by the pixelization. This problem can be eliminated by heavily oversampling the map, but is exacerbated by the fact that the E power spectrum is expected to be much larger than the B power spectrum and extremely blue. We found that a factor of 2 to 3 more pixels are needed in a polarization map to achieve the same level of contamination by aliased power than in a temperature map.

Christoph Schmid, Theoretische Physik ETH

Cosmological Vorticity Perturbations and Mach's Principle  

We consider cosmological vorticity perturbations on a spatially flat FRW cosmology, and we ask: will cosmological rotational perturbations exactly drag the axis of a gyroscope (and the local inertial frames) relative to the geodesics to galaxies beyond the perturbation? We write the laws of gravitomagnetism in a form showing clearly the close correspondence with Ampere's law of ordinary magnetism. Our results (valid for any equation of state):
1. The dragging of a gyroscope axis by rotational perturbations beyond the Hubble-dot radius is exponentially suppressed.
2.For the special case of a homogeneous rotation of cosmological matter inside a given perturbation radius, the dragging of the axis of a gyroscope at the center approaches exact dragging exponentially fast as the perturbation radius increases beyond the Hubble-dot radius.
3.For a general vorticity perturbation a gyroscope axis exactly follows the (dr/r)-average of the gravitomagnetic moments of the energy current of cosmological matter with the exponential cutoff at the Hubble-dot radius.
In this precise sense Mach's Principle on nonrotating frames follows from perturbed FRW cosmology with Einstein Gravity.