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Kitaura Joyanes, Francisco Shu (2007): Cosmic cartography: Bayesian reconstruction of the cosmological large-scale structure. Dissertation, LMU München: Faculty of Physics
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Abstract

The cosmic origin and evolution is encoded in the large-scale matter distribution observed in astronomical surveys. Galaxy redshift surveys have become in the recent years one of the best probes for cosmic large-scale structures. They are complementary to other information sources like the cosmic microwave background, since they trace a different epoch of the Universe, the time after reionization at which the Universe became transparent, covering about the last twelve billion years. Regarding that the Universe is about thirteen billion years old, galaxy surveys cover a huge range of time, even if the sensitivity limitations of the detectors do not permit to reach the furthermost sources in the transparent Universe. This makes galaxy surveys extremely interesting for cosmological evolution studies. The observables, galaxy position in the sky, galaxy ma gnitude and redshift, however, give an incomplete representation of the real structures in the Universe, not only due to the limitations and uncertainties in the measurements, but also due to their biased nature. They trace the underlying continuous dark matter field only partially being a discrete sample of the luminous baryonic distribution. In addition, galaxy catalogues are plagued by many complications. Some have a physical foundation, as mentioned before, others are due to the observation process. The problem of reconstructing the underlying density field, which permits to make cosmological studies, thus requires a statistical approach. This thesis describes a cosmic cartography project. The necessary concepts, mathematical frame-work, and numerical algorithms are thoroughly analyzed. On that basis a Bayesian software tool is implemented. The resulting Argo-code allows to investigate the characteristics of the large-scale cosmological structure with unprecedented accuracy and flexibility. This is achieved by jointly estimating the large-scale density along with a variety of other parameters ---such as the cosmic flow, the small-scale peculiar velocity field, and the power-spectrum--- from the information provided by galaxy redshift surveys. Furthermore, Argo is capable of dealing with many observational issues like mask-effects, galaxy selection criteria, blurring and noise in a very efficient implementation of an operator based formalism which was carefully derived for this purpose. Thanks to the achieved high efficiency of Argo the application of iterative sampling algorithms based on Markov Chain Monte Carlo is now possible. This will ultimately lead to a full description of the matter distribution with all its relevant parameters like velocities, power spectra, galaxy bias, etc., including the associated uncertainties. Some applications are shown, in which such techniques are used. A rejection sampling scheme is successfully applied to correct for the observational redshift-distortions effect which is especially severe in regimes of non-linear structure formation, causing the so-called finger-of-god effect. Also a Gibbs-sampling algorithm for power-spectrum determination is presented and some preliminary results are shown in which the correct level and shape of the power-spectrum is recovered solely from the data. We present in an additional appendix the gravitational collapse and subsequent neutrino-driven explosion of the low-mass end of stars that undergo core-collapse Supernovae. We obtain results which are for the first time compatible with the Crab Nebula.