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UBC Theses and Dissertations

A study of numerical errors in simulations of the cosmic microwave background polarization Chen, Bell I. L.

Abstract

There have been numerous studies of data analysis issues involving temperature anisotropics on the microwave sky, but far less attention paid to the polarization signals. The production of maps and their reduction to power spectra proceeds by choosing a particular way of dividing the sphere into pixels. The Equidistant Cylindrical Projection (ECP) is the geometrically simplest pixelization scheme and might have been sufficient in the early days of Cosmology, when the uncertainties from numerical calculations were ususally overshadowed by experimental errors. But with future satellite missions (MAP and Planck) on the horizon, we need to make sure that the pixelization scheme we choose does not add to the small experimental errors, in order to determine the cosmological parameters as accurately as possible. Numerical errors are a small part of the whole polarization data analysis process but one that is easily dealt with in comparison to other more complicated analyses of polarization. In this thesis, we begin by stating a consistent set of equations for calculating the CMB polarization sky and power spectrum. This will be implemented into an ECP scheme, which allows us to study the numerical errors introduced by various effetcs related to pixelization. We will show that all these errors can be optimally reduced by numerical techniques. And finally, we will apply these techniques to a HEALPix pixelization scheme to obtain the most accurate polarization power spectra.

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