Book Description

The thesis concerns the statistical characterisation of large scale properties of the Universe. Two complementary data sets are considered: all-sky maps of the cosmic microwave background (CMB) temperature fluctuations from the Wilkinson Microwave Anisotropy Probe (WMAP); and large area maps of galaxies detected through the sub-millimetre electromagnetic emission using the Herschel Space Observatory. The standard model predicts the distribution of temperature fluctuations in the CMB to be Gaussian, homogeneous and isotropic. Since they could deviate from the standard model in many different ways, a number of complementary descriptors are required. All-sky maps of the CMB are often decomposed into spherical harmonic modes. Any modes aligned with the Galactic plane are particularly interesting because anomalous behaviour in them could indicate errors in the subtraction of Galactic foreground. Here a simple statistical analysis of these modes is tested and shown to be a useful diagnostic of possible foreground subtraction systematics. In addition, two methods for characterizing large-scale anisotropy in all sky CMB maps are discussed. They are tested against simulated anisotropic cosmologies and both show promise as effective diagnostic tools. The second part concerns analytical models of the correlation function for the distribution of galaxies. The 'Halo' model is comprehensive, but it is also rather complex. We promote a simpler alternative based on fitting functions found from numerical simulations. Both models compare well to the observational data, showing that the fitting function method can be a quick and easy option. Also, we show that a 'key' Halo model assumption, intra-halo correlations, is not required to produce a good fit. We summarise by discussing the different approximations used in the current galaxy clustering models, the limits of the currently available data and future areas of development.