Cosmic cartography

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.