Redshift evolution of clustering

Abstract

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.

Joint measurement of lensing–galaxy correlations using SPT and DES SV data

“…At some level, uncertainty in the nonlinear matter power spectrum is incorporated into our analysis through our modeling of the tracer bias, as we discuss in more detail below. A common approach to parameterizing b(k, χ) is the socalled linear bias model (Mo & White 1996;Matarrese et al 1997), for which the bias has no scale dependence, but is allowed to vary with comoving distance: b(k, χ) = f (χ). It is well known that the linear bias model accurately describes galaxy clustering over scales where the matter density perturbations are linear, and even at scales several times smaller than the transition scale from the linear to the nonlinear regime (e.g.…”

“…Bielefeld et al 2015) and redshift dependence (e.g. Fry 1996;Matarrese et al 1997;Clerkin et al 2015) of the bias have been proposed in the literature. Since we are only attempting to capture small deviations from linear bias, a Taylor expansion in k is appropriate here.…”

A large narrow-band Hα survey at z∼ 0.2: the bright end of the luminosity function, cosmic variance and clustering across cosmic time

“…The bias parameter b(z) describes how the matter distribution traces the DM distribution, as function of redshift. In the bias model of Matarrese et al (1997), the physical parameters of galaxies are determined by their host dark matter halo mass. In such a model, b(z) depends on the minimum mass of the DM halo.…”

Upper limits on neutrino masses from the 2dFGRS and WMAP: the role of priors

“…Hierarchical merging scenarios also suggest a more complicated picture of biasing as it could be non-linear, scale-dependent and stochastic (e.g. [38,56,57,58,59,60,61]. But is the biasing still scale-dependent at the large scales (k −1 > 7 h −1 Mpc) where we analyse the 2dFGRS power spectrum ?…”