Temperature and Polarization Studies of the Cosmic Microwave Background

Abstract

The cosmic microwave background (CMB) provides us with a wealth of information about the properties of our Universe. In this PhD work, we develop and apply new techniques for studying fundamental problems of cosmology using the CMB. Dark energy, if it exists, leaves a characteristic imprint in the CMB temperature fluctuations, the so-called integrated Sachs-Wolfe (ISW) effect. This small effect can be detected via its cross-correlation with the large-scale structure (LSS). We derive an optimal method for ISW detection using temperature and polarization data of the CMB which differs from that usually used in two fundamental ways: we keep the LSS distribution and a part of the primordial temperature fluctuations fixed, rather than averaging over different realisations as done in the standard method. For an ideal scenario, we obtain an overall enhancement of the detection significance of 23 per cent. For polarization data from the Planck Surveyor mission, this enhancement will be at least 10 per cent, where the limiting factor will be the contamination by Galactic foregrounds. The CMB is observed to be almost perfectly isotropic, which is considered strong evidence for the isotropy of the Universe. However, some anomalies have been found in the temperature map of the Wilkinson Microwave Anisotropy Probe (WMAP), which seem to question the statistical isotropy of the temperature fluctuations. In order to understand whether these are due to chance fluctuations or to a preferred direction intrinsic to the geometry of the primordial Universe, we compute the part of the WMAP polarization map which is uncorrelated with the temperature map, and use it as a statistically independent probe of the so-called axis of evil. The latter is an unusual alignment between the preferred directions of the quadrupole and the octopole in the temperature map. We find that the axis of the quadrupole of the uncorrelated polarization map aligns with the axis of evil, whereas the axis of the octopole does not. However, due to the high noise-level in the WMAP polarization map, we have an uncertainty of about 45 deg in our axes. With this uncertainty, the probability of at least one axis aligning by chance in an isotropic Universe is around 50 per cent. We therefore do not obtain evidence for or against a preferred direction intrinsic to the primordial Universe. For Planck, we expect the uncertainty in the axes to go down to 10-20 deg, again depending on how well the foregrounds can be removed from the map. Our technique applied to Planck data will thus serve as a powerful means to understand the origin of the CMB anomalies. Instead of studying particular features in the CMB maps as described above, we can also use the CMB to constrain several cosmological parameters simultaneously by sampling the parameter space. The parameter constraints obtained by WMAP marked the beginning of precision cosmology and were the biggest success of the mission. In such parameter sampling studies, the main bottleneck is usually the evaluation of the likelihood. We have thus implemented a sparse-grids based interpolation of the WMAP likelihood surface as a shortcut for the likelihood evaluation. This is orders of magnitude faster to compute than the original likelihood. Our method is a competitive alternative to other approaches for speeding up parameter sampling.

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