Cluster Abundance Constraints on Quintessence Models

TL;DR

This paper derives a general expression for cluster abundance constraints on cosmological models with dark matter and quintessence, combining observational data to identify best-fitting parameters and exploring model evolution.

Contribution

It provides a new, general formula for the cluster abundance constraint parameter , , applicable to a wide range of dark energy models including quintessence.

Findings

Derived a general  expression for various models.

Combined cluster and COBE data to constrain model parameters.

Discussed constraints from cluster evolution.

Abstract

The abundance of rich clusters is a strong constraint on the mass power spectrum. The current constraint can be expressed in the form $\sigma_8 \Omega_m^{\gamma} = 0.5 \pm 0.1$ where $\sigma_8$ is the $rms$ mass fluctuation on 8 $h^{-1}$ Mpc scales, $\Omega_m$ is the ratio of matter density to the critical density, and $\gamma$ is model-dependent. In this paper, we determine a general expression for $\gamma$ that applies to any models with a mixture of cold dark matter plus cosmological constant or quintessence (a time-evolving, spatially-inhomogeneous component with negative pressure) including dependence on the spectral index $n$, the Hubble constant $h$, and the equation-of-state of the quintessence component $w$. The cluster constraint is combined with COBE measurements to identify a spectrum of best-fitting models. The constraint from the evolution of rich clusters is also discussed.