Redshift Evolution of Clustering

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. In an illustration of this formalism, assuming a simple phenomenological model for the initial power spectrum and an Einstein-de Sitter cosmological model, we find that the linear bias factor b generally evolves strongly with z if b> at the present epoch. We make a detailed comparison between the output of this approach and the spatial, angular and projected correlation functions from different samples of high-redshift objects: QSOs from the Durham/AAT catalogue and galaxies from the CFRS, Keck K-band and HDF samples. 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 at z=0 is small. Our results chiefly demonstrate that, even if the background cosmology and mass power spectrum are completely specified, there remains a large and uncertain effect connected with the evolution of the bias. Until a more complete theory of biasing is developed, this uncertainty will continue to complicate the cosmological interpretation of clustering evolution data.