Local Methods for the Cosmic Microwave Background
Author(s)
Bowyer, Jude William
Type
Thesis or dissertation
Abstract
The standard tools for analyzing the Cosmic Microwave Background (CMB), a
key component for making cosmological inferences, are usually of global sampling
type. Such a methodological bias may preclude the development of important
techniques for cosmology. This thesis develops local, real-space tools for
CMB analysis which may be complemented using harmonic space techniques or
provide useful signal diagnostics on their own.
Particularly, finite-difference schemes for performing local derivatives are investigated.
One can define derivatives which extract the primordial polarization
modes from the measured CMB Stokes parameters by constructing real scalar and
pseudo-scalar fields. The detection of a primordial curl-like (‘B’-mode) CMB polarization
signal would imply the existence of a background of primordial gravitational
waves, the ‘smoking gun’ signal of an inflationary cosmology. On an obscured
(masked) sky, the gradient-like (‘E’-mode) signal leaks into the B-mode
signal when the standard harmonic E/B signal decomposition is performed —
using local techniques instead, this leakage can be reduced since the masked region
is not sampled from. An algorithm and a software package are developed
for just such a calculation. Furthermore, differencing errors in the presence of
discontinuous signals are utilized to produce the ‘Laplacian-difference’ method,
which enhances pathological and discontinuous signals. Such signals, in the absence
of systematics, might reveal the presence of cosmic defects.
The scalar and pseudo-scalar fields produced will feature self-coupled modetransfer
due to masking; the mode-transfer matrices are related to the optimal
apodization schemes for extracting power spectra. The transfer matrices for various
spectral operations on scalar fields are presented, which for the polarization
spectra provide important computational advantages over the direct utilization
of the E- and B-modes.
key component for making cosmological inferences, are usually of global sampling
type. Such a methodological bias may preclude the development of important
techniques for cosmology. This thesis develops local, real-space tools for
CMB analysis which may be complemented using harmonic space techniques or
provide useful signal diagnostics on their own.
Particularly, finite-difference schemes for performing local derivatives are investigated.
One can define derivatives which extract the primordial polarization
modes from the measured CMB Stokes parameters by constructing real scalar and
pseudo-scalar fields. The detection of a primordial curl-like (‘B’-mode) CMB polarization
signal would imply the existence of a background of primordial gravitational
waves, the ‘smoking gun’ signal of an inflationary cosmology. On an obscured
(masked) sky, the gradient-like (‘E’-mode) signal leaks into the B-mode
signal when the standard harmonic E/B signal decomposition is performed —
using local techniques instead, this leakage can be reduced since the masked region
is not sampled from. An algorithm and a software package are developed
for just such a calculation. Furthermore, differencing errors in the presence of
discontinuous signals are utilized to produce the ‘Laplacian-difference’ method,
which enhances pathological and discontinuous signals. Such signals, in the absence
of systematics, might reveal the presence of cosmic defects.
The scalar and pseudo-scalar fields produced will feature self-coupled modetransfer
due to masking; the mode-transfer matrices are related to the optimal
apodization schemes for extracting power spectra. The transfer matrices for various
spectral operations on scalar fields are presented, which for the polarization
spectra provide important computational advantages over the direct utilization
of the E- and B-modes.
Date Issued
2011
Online Publication Date
2011-11-28T16:44:59Z
Date Awarded
2011-11
Advisor
Jaffe, Andrew
Creator
Bowyer, Jude William
Publisher Department
Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)