The amplitude of mass fluctuations

Neta A. Bahcall, Paul Bode

Research output: Contribution to journalArticlepeer-review

56 Scopus citations


We determine the linear amplitude of mass fluctuations in the universe, σ8, from the abundance of massive clusters at redshifts z = 0.5-0.8. The evolution of massive clusters depends exponentially on the amplitude of mass fluctuations and thus provides a powerful measure of this important cosmological parameter. The relatively high abundance of massive clusters observed at z > 0.5 and the relatively slow evolution of their abundance with time suggest a high amplitude of mass fluctuations: σ 8 = 0.9 (±10%) for Ωm = 0.4, increasing slightly to σ8 = 0.95 for Ωm = 0.25 and σ8 = 1.0 for Ωm = 0.1 (flat cold dark matter models). We use the cluster abundance observed at z = 0.5-0.8 to derive a normalization relation from the high-redshift clusters, which is only weakly dependent on Ωm: σ8Ωm 0.14 = 0.78 ± 0.08. When combined with recent constraints from the present-day cluster mass function, σ8Ω m0.6 = 0.33 ± 0.03, we find σ8 = 0.98 ± 0.1 and Ωm = 0.17 ± 0.05. Low-σ 8 values (≲0.7) are unlikely; they produce an order-of-magnitude fewer massive clusters than observed.

Original languageEnglish (US)
Pages (from-to)L1-L4
JournalAstrophysical Journal
Issue number1 II
StatePublished - May 1 2003

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Cosmological parameters
  • Galaxies: clusters: general


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