Non-Gaussian density fields and their signatures in redshift surveys
Stirling, Alison Janet
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The wealth of structure observed from galactic to super-cluster scales is believed to have formed through the gravitational collapse of tiny inhomogeneities that existed in the m atter field in the early universe. The origin of these inhomogeneities, however, is still a m atter of debate, and there are a number of theories that set out to explain their initiation. A possible distinguishing factor between these theories is the nature of the distribution of the primordial density fluctuations.This thesis is concerned with the measurement of the statistics of density fluctuations from redshift surveys with a view to placing constraints on the distribution of fluctuations in the primordial density field. The first approach considered is the effect of different statistical distributions on the evolution of the power spectrum into the highly nonlinear regime. This has been explored by running N-body simulations with different non-Gaussian initial conditions, and comparing the locus of evolution from the linear to the non-linear power spectrum with that derived for initially Gaussian fields. The evolution of power for a field with x 2 initial conditions is used to form a test for the viability of an isocurvature %2 model which has been proposed in the literature. Higher order moments of evolved simulations of this model under various biasing schemes are then compared with existing measurements of higher order moments from the APM galaxy survey.aving investigated the evolution of the power spectrum of initially non-Gaussian fields, a natural progression is to consider higher order Fourier statistics as a test for non- Gaussian fields. A four-point Fourier based test is developed in which correlations between the amplitude squared of the density modes (power modes) are compared with the Gaussian prediction, which is a function of the selection function only. The test has been applied to the combined QDOT and 1.2 Jy redshift surveys, and the results have enabled quantitative limits to be placed on a particular class of non-Gaussian models. The projected increase in sensitivity of the test for forthcoming surveys has also been calculated.The power correlations test is to some degree affected by redshift distortions, and extensions to the test are developed to take into account their effect for spherical redshift surveys. The emphasis is then shifted, and the correlations between Fourier modes are used as a new method for measuring the redshift distortion parameter, ¡3. This approach does not rely on the distant observer approximation, and extensions have been made to deal with the mildly non-linear regime, in which the randomised velocities of galaxies in clusters damp the linear redshift distortions, and form the so called ‘fingers of god’. The method is applied to an ensemble of simulations to test its reliability, including some mock QDOT+1.2 Jy and PSCz surveys. Finally, the test is applied to the real QDOT+1.2 Jy survey, and an estimate found for the redshift distortion parameter, Β.