Cosmological Redshift Distortion of Correlation Functions as a Probe of the Density Parameter and the Cosmological Constant

TL;DR

The paper addresses using cosmological redshift-space distortions of galaxy and quasar clustering to jointly constrain the density parameter $Ω_0$ and the cosmological constant $λ_0$. It extends linear theory distortions to nonzero curvature, defining $β(z)=f(z)/b(z)$ and $η(z)=c_{∥}(z)/c_{⊥}(z)$, and derives an anisotropic correlation function $ξ^{(s)}(s_ot,s_ orth)$ in terms of the real-space $ξ^{(r)}$ with multipole contributions. It argues that while low-$z$ galaxy distortions mainly probe $Ω(z)^{0.6}$ through $β$, high-$z$ quasar distortions offer sensitivity to $λ_0$ via the redshift dependence of $f(z)$ and geometric distortion, and provides predictions for CDM and power-law models to illustrate discriminating among $λ_0$ models. The work highlights the potential of upcoming surveys (e.g., SDSS, 2dF) to measure these distortions and thereby extract cosmological parameters from anisotropic clustering data, while noting the need for nonlinear extensions and systematic studies.

Abstract

We propose cosmological redshift-space distortion of correlation functions of galaxies and quasars as a probe of both the density parameter $Ω_0$ and the cosmological constant $λ_0$. In particular, we show that redshift-space distortion of quasar correlation functions at $z\sim2$ can in principle set a constraint on the value of $λ_0$. This is in contrast to the popular analysis of galaxy correlation functions in redshift space which basically determines $Ω_0^{0.6}/b$, where $b$ is the bias parameter, but is insensitive to $λ_0$. For specific applications, we present redshift-space distortion of correlation functions both in cold dark matter models and in power-law correlation function models, and discuss the extent to which one can discriminate between the different $λ_0$ models.