Optically selected galaxy clusters as a cosmological probe

Multi-wavelength large-scale surveys are currently exploring the
Universe and establishing the cosmological scenario with
extraordinary accuracy. There has been recently a significant
theoretical and observational progress in efforts to use clusters
of galaxies as probes of cosmology and to test the physics of
structure formation. Galaxy clusters are the most massive
gravitationally bound systems in the Universe, which trace the
evolution of the large-scale structure. Their number density and
distribution are highly sensitive to the underlying cosmological
model. The constraints on cosmological parameters which result from
observations of galaxy clusters are complementary with those from
other probes. This dissertation examines the crucial role of
clusters of galaxies in confirming the standard model of cosmology,
with a Universe dominated by dark matter and dark energy. In
particular, we examine the clustering of optically selected galaxy
clusters as a useful addition to the common set of cosmological
observables, because it extends galaxy clustering analysis to the
high-peak, high-bias regime. The clustering of galaxy clusters
complements the traditional cluster number counts and
observable-mass relation analyses, significantly improving their
constraining power by breaking existing calibration degeneracies.
We begin by introducing the fundamental principles at the base of
the concordance cosmological model and the main observational
evidence that support it. We then describe the main properties of
galaxy clusters and their contribution as cosmological probes. We
then present the theoretical framework of galaxy clusters number
counts and power spectrum. We revise the formulation and
calibration of the halo mass function, whose high mass tail is
populated by galaxy clusters. In addition to this, we give a
prescription for modelling the cluster redshift space power
spectrum, including an effective modelling of the weakly non-linear
contribution and allowing for an arbitrary photometric redshift
smoothing. Some definitions concerning the study of non-Gaussian
initial conditions are presented, because clusters can provide
constraints on these models. We dedicate a Chapter to the data we
use in our analysis, namely the Sloan Digital Sky Survey maxBCG
optical catalogue. We describe the data sets we derived from this
large sample of clusters and the corresponding error estimates.
Specifically, we employ the cluster abundances in richness bins,
the weak-lensing mass estimates and the redshift-space power
spectrum, with their respective covariance matrices. We also relate
the cluster masses to the observable quantity (richness) by means
of an empirical scaling relation and quantify its scatter. In the
next Chapter we present the results of our Monte Carlo Markov Chain
analysis and the cosmological constraints obtained. With the maxBCG
sample, we simultaneously constrain cosmological parameters and
cross-calibrate the mass-observable relation. We find that the
inclusion of the power spectrum typically brings a 50% improvement
in the errors on the fluctuation amplitude and the matter density.
Constraints on other parameters are also improved, even if less
significantly. In addition to the cluster data, we also use the CMB
power spectra from WMAP7, which further tighten the confidence
regions. We also apply this method to constrain models of the early
universe through the amount of primordial non-Gaussianity of the
initial density perturbations (local type) obtaining consistent
results with the latest constraints. In the last Chapter, we
introduce some preliminary calculations on the cross-correlation
between clusters and galaxies, which can provide additional
constraining power on cosmological models. In conclusion, we
summarise our main achievements and suggest possible future
developments of research.