Related papers: Power Spectrum, Bispectrum, 2- and 3-Point Correla…
We explore the correlations between correlation functions of the primordial curvature perturbation produced during inflation. We find that for general single field inflation, other than the source terms which depend on the model details,…
Small- and intermediate-scale galaxy clustering can be used to establish the galaxy-halo connection to study galaxy formation and evolution and to tighten constraints on cosmological parameters. With the increasing precision of galaxy…
The two-point correlation function (2PCF) is the most widely used tool for quantifying the spatial distribution of galaxies. Since the distribution of galaxies is determined by galaxy formation physics as well as the underlying cosmology,…
The gravitational clustering of collisionless particles in an expanding universe is modelled using some simple physical ideas. I show that it is possible to understand the nonlinear clustering in terms of three well defined regimes: (1)…
Understanding the large-scale structure of the Universe requires analyses of cosmic clustering and its evolution over time. In this work, we investigate the clustering properties of SDSS blue galaxies, which are excellent tracers of dark…
Cosmological correlation functions contain valuable information about the primordial Universe, with possible signatures of new massive particles at very high energies. Recent developments, including the cosmological bootstrap, bring new…
The three-point correlation function (3PCF) can now be measured in large galaxy redshift surveys, but in three dimensions its interpretation is complicated by the presence of redshift-space distortions. I investigate the projected 3PCF,…
This thesis is centered on three main subjects within the theory of inflation and cosmological perturbations: loop corrections to the power spectrum of curvature fluctuations generated during inflation; evolution of cosmological…
The non-Gaussianity of inflationary perturbations, as encoded in the bispectrum (or 3-point correlator), has become an important additional way of distinguishing between inflation models, going beyond the linear Gaussian perturbation…
Conventional estimators of the anisotropic power spectrum and two-point correlation function (2PCF) adopt the `Yamamoto approximation', fixing the line-of-sight of a pair of galaxies to that of just one of its members. Whilst this is…
The purpose of our study is to understand the mathematical origin in real space of modulated and damped sinusoidal peaks observed in cosmic microwave background radiation anisotropies. We use the theory of the Fourier transform to connect…
We use rich clusters of galaxies in the Northern and Southern Galactic hemispheres up to a redshift z=0.12 to determine the cluster correlation function. We show that superclusters of galaxies and voids between them form a moderately…
The connection between the two-point and the three-point correlation functions in the non-linear gravitational clustering regime is studied. Under a scaling hypothesis, we find that the three-point correlation function, $\zeta$, obeys the…
We analyze the consequences of models of structure formation for higher-order ($n$-point) galaxy correlation functions in the mildly non-linear regime. Several variations of the standard $\Omega=1$ cold dark matter model with…
In this pedagogical lecture, I introduce some of the basic terminology and description of fluctuating fields as they occur on cosmology. I define various statistical, cosmological and sample homogeneity and explain what is meant by the fair…
The determination of the inflationary energy scale represents one of the first step towards the understanding of the early Universe physics. The (very mild) non-Gaussian signals that arise from any inflation model carry information about…
We analyze the 2-point correlation function (2PCF) of galaxy groups identified from the 2-degree Field Galaxy Redshift Survey with the halo based group finder recently developed by Yang et al (2004b). With this group catalogue we are able…
We propose a holographic description of four-dimensional single-scalar inflationary universes, and show how cosmological observables, such as the primordial power spectrum, are encoded in the correlation functions of a three-dimensional…
We investigate the nonlinear two- and three-point correlation functions of the cosmological density field in Fourier space and test the popular hierarchical clustering model, that the three-point amplitude Q is independent of scale. In…
The power spectrum has long been the workhorse summary statistics for large-scale structure cosmological analyses. However, gravitational non-linear evolution moves precious cosmological information from the two-point statistics (such as…