No abstract

The evolution of galaxy clustering from z=0 to z~=4.5 is analysed using the angular correlation function and the photometric redshift distribution of galaxies brighter than IAB<=28.5 in the Hubble Deep Field North. The reliability of the photometric redshift estimates is discussed on the basis of the available spectroscopic redshifts, comparing different codes and investigating the effects of photometric errors. The redshift bins in which the clustering properties are measured are then optimized to take into account the uncertainties of the photometric redshifts. The results show that the comoving correlation length r0 has a small decrease in the range 0<~z<~1 followed by an increase at higher z. We compare these results with the theoretical predictions of a variety of cosmological models belonging to the general class of Cold Dark Matter scenarios, including Einstein-de Sitter models, an open model and a flat model with non-zero cosmological constant. Comparison with the expected mass clustering evolution indicates that the observed high-redshift galaxies are biased tracers of the dark matter with an effective bias b strongly increasing with redshift. Assuming an Einstein-de Sitter universe, we obtain b~=2.5 at z~=2 and b~=5 at z~=4. These results support theoretical scenarios of biased galaxy formation in which the galaxies observed at high redshift are preferentially located in more massive haloes. Moreover, they suggest that the usual parameterization of the clustering evolution as ξ(r,z)=ξ(r,0)(1+z)-(3+ɛ) is not a good description for any value of ɛ. Comparison of the clustering amplitudes that we measured at z~=3 with those reported by Adelberger et al. and Giavalisco et al., based on a different selection, suggests that the clustering depends on the abundance of the objects: more abundant objects are less clustered, as expected in the paradigm of hierarchical galaxy formation. The strong clustering and high bias measured at z~=3 are consistent with the expected density of massive haloes predicted in the frame of the various cosmologies considered here. At z~=4, the strong clustering observed in the Hubble Deep Field requires a significant fraction of massive haloes to be already formed by that epoch. This feature could be a discriminant test for the cosmological parameters if confirmed by future observations

We analyze the temperature three-point correlation function and the skewness of the Cosmic Microwave Background (CMB), providing general relations in terms of multipole coefficients. We then focus on applications to large angular scale anisotropies, such as those measured by the COBE DMR, calculating the contribution to these quantities from primordial, inflation generated, scalar perturbations, via the Sachs-Wolfe effect. Using the techniques of stochastic inflation we are able to provide a universal expression for the ensemble averaged three-point function and for the corresponding skewness, which accounts for all primordial second-order effects. These general expressions would moreover apply to any situation where the bispectrum of the primordial gravitational potential has a hierarchical form. Our results are then specialized to a number of relevant models: power-law inflation driven by an exponential potential, chaotic inflation with a quartic and quadratic potential and a particular case of hybrid inflation. In all these cases non-Gaussian effects are small: as an example, the mean skewness is much smaller than the cosmic rms skewness implied by a Gaussian temperature fluctuation field.

We discuss how the redshift dependence of the observed two-point correlation function of various classes of objects can be related to theoretical predictions. This relation involves first a calculation of the redshift evolution of the underlying matter correlations. The next step is to relate fluctuations in mass to those of any particular class of cosmic objects; in general terms, this means a model for the bias and how it evolves with cosmic epoch. Only after these two effects have been quantified can one perform an appropriate convolution of the non-linearly evolved two-point correlation function of the objects with their redshift distribution to obtain the 'observed' correlation function for a given sample. This convolution in itself tends to mask the effect of evolution by mixing amplitudes at different redshifts. We develop a formalism which incorporates these requirements and, in particular, a set of plausible models for the evolution of the bias factor. We apply this formalism to the spatial, angular and projected correlation functions from different samples of highredshift objects, assuming a simple phenomenological model for the initial power-spectrum and an Einstein-de Sitter cosmological model. We find that our model is roughly consistent with data on the evolution of QSO and galaxy clustering, but only if the effective degree of biasing is small. We discuss the differences between our analysis and other theoretical studies of clustering evolution and argue that the dominant barrier to making definitive predictions is uncertainty about the appropriate form of the bias and its evolution with cosmic epoch.