[Paper Review] Constraining Omega with Cluster Evolution

Neta A. Bahcall, X. Fan+1 more|CERN Bulletin|Jun 3, 1997

Astronomy and Astrophysical Research4 citations

TL;DR

This paper uses the evolution of rich galaxy cluster abundance from z ≈ 0 to z ≈ 0.5–1 to break the degeneracy between Omega (cosmic mass density) and sigma_8 (power spectrum normalization). By comparing observed cluster evolution with theoretical models, it finds Omega = 0.3 ± 0.1 and sigma_8 = 0.85 ± 0.15, indicating a low-density, low-bias universe, with implications for cosmological model selection.

ABSTRACT

We show that the evolution of the number density of rich clusters of galaxies breaks the degeneracy between Omega (the mass density ratio of the universe) and sigma_{8} (the normalization of the power spectrum), sigma_{8}Omega^{0.5} \simeq 0.5, that follows from the observed present-day abundance of rich clusters. The evolution of high-mass (Coma-like) clusters is strong in Omega=1, low-sigma_{8} models (such as the standard biased CDM model with sigma_{8} \simeq 0.5), where the number density of clusters decreases by a factor of \sim 10^{3} from z = 0 to z \simeq 0.5; the same clusters show only mild evolution in low-Omega, high-sigma_{8} models, where the decrease is a factor of \sim 10. This diagnostic provides a most powerful constraint on Omega. Using observations of clusters to z \simeq 0.5-1, we find only mild evolution in the observed cluster abundance. We find Omega = 0.3 \pm 0.1 and sigma_{8} = 0.85 \pm 0.15 (for Lambda = 0 models; for Omega + Lambda = 1 models, Omega = 0.34 \pm 0.13). These results imply, if confirmed by future surveys, that we live in a low-den sity, low-bias universe.

Motivation & Objective

• To break the degeneracy between Omega and sigma_8 using cluster evolution data.
• To determine the cosmic mass density Omega using observed evolution of high-mass clusters to z ≈ 0.5–1.
• To test whether the observed mild evolution in cluster abundance favors low-Omega or high-Omega models.
• To constrain cosmological parameters in Lambda = 0 and Omega + Lambda = 1 models.

Proposed method

• Modeling the evolution of rich cluster number density in different cosmological models (Omega = 1 vs. low-Omega).
• Comparing theoretical predictions of cluster abundance evolution with observational data up to z ≈ 0.5–1.
• Using the strong evolution in high-mass clusters in Omega = 1, low-sigma_8 models (e.g., standard CDM with sigma_8 ≈ 0.5) versus mild evolution in low-Omega, high-sigma_8 models.
• Applying the diagnostic that cluster evolution breaks the Omega–sigma_8 degeneracy, enabling tighter constraints.
• Fitting observed cluster counts to theoretical models to derive constraints on Omega and sigma_8.

Experimental results

Research questions

• RQ1 How does the evolution of rich cluster abundance constrain the cosmic mass density Omega?
• RQ2 Can cluster evolution break the degeneracy between Omega and sigma_8?
• RQ3 Which cosmological model—high-Omega or low-Omega—best matches observed cluster evolution to z ≈ 0.5–1?
• RQ4 What are the implications for the bias of galaxy formation if Omega is low?

Key findings

• The observed cluster abundance shows only mild evolution from z ≈ 0 to z ≈ 0.5–1, inconsistent with strong evolution expected in Omega = 1, low-sigma_8 models.
• The data favor a low-Omega universe, yielding Omega = 0.3 ± 0.1 for Lambda = 0 models.
• For models with Omega + Lambda = 1, the result is Omega = 0.34 ± 0.13.
• The derived sigma_8 is 0.85 ± 0.15, significantly higher than the standard CDM value of ~0.5.
• The results imply a low-bias, low-density universe if confirmed by future surveys.