Astronomy and Astrophysics – Astrophysics
Scientific paper
1998-04-02
Astrophys.J.508:483-490,1998
Astronomy and Astrophysics
Astrophysics
19 pages, 4 figures, submitted to ApJ
Scientific paper
10.1086/306436
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.
Steinhardt Paul J.
Wang Limin
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