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Cited by 159Cosmology and Gravitation TheoriesGalaxies: Formation, Evolution, PhenomenaDark Matter and Cosmic Phenomena

Why Is the Cosmic Microwave Background Fluctuation Level 10−5?

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Tegmark, Max, Rees, Martin J.·1998·The Astrophysical Journal
DOI 10.1086/305673
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Abstract

We explore the qualitative changes that would occur if the amplitude Q ~ 10 -5 of cosmological density fluctuations were different. If Q ≲ 10 -6 , the cosmological objects that form would have such low virial temperatures that they may be unable to cool and form stars, and they would be so loosely bound that even if they could produce a supernova explosion they might be unable to retain the heavy elements necessary for planetary life. If Q ≳ 10 -4 , dense supermassive galaxies would form, and biological evolution could be marred by short disruption timescales for planetary orbits. If Q were still larger, most bound systems would collapse directly to supermassive black holes. These constraints on Q can be expressed in terms of fundamental constants alone and depend only on the electromagnetic and gravitational coupling constants, the electron-proton mass ratio, and the matter-to-photon ratio. We discuss the implications for inflation and defect models and note that the recent anthropic upper bounds on the cosmological constant Λ would be invalid if both Q and Λ could vary and there were no anthropic constraints on Q . The same applies to anthropic bounds on the curvature parameter Ω.

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Integrity signals

Registry

Crossref · 10.1086/305673

Cites

47 of 47 references verified0 citation errors · 0 not checkable

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  • The life-permitting range for Q is given by the inequality (3) derived by Tegmark & Rees (1998).

    “Tegmark & Rees (1998) were the first to calculate the range of Q which permits life, deriving the following limits for the case where r L ¼ 0:”

    From The Fine-Tuning of the Universe for Intelligent Life (2012) · cites this paper as Tegmark & Rees (1998)

    Section 3 derives an approximate upper limit of Q ≲ 10⁻⁴, and Section 6 identifies cooling difficulties below Q ≈ 10⁻⁶; the paper says its main analysis assumes a flat universe with zero cosmological constant. But Section 6 explicitly allows that life might arise at more extreme Q values, so these are not strict life-permitting bounds. Our copy also does not establish the claim that Tegmark and Rees were the first to calculate them. (LLM, conf=0.85)

    Experimental — accuracy not yet measured

  • It is not clear whether the cold big bang island connects to the hot big bang island (10^6 < Z_g < 10^11) investigated by Tegmark & Rees (1998).

    “Aguirre (2001) only considers the case Z g , 1 in detail, so it is not clear whether the CBB island connects to the HBB island (10 6 t Z g t 10 11 ) investigated by Tegmark & Rees (1998).”

    From The Fine-Tuning of the Universe for Intelligent Life (2012) · cites this paper as Tegmark & Rees (1998)

    Section 6 (Discussion; page unavailable) says Tegmark and Rees explored cosmological scenarios with different values of Q. Section 2.1 (Notation; page unavailable) gives a baryon-to-photon ratio, but our copy does not identify a hot-big-bang island with 10^6 < Z_g < 10^11. Searches for Z_g, that interval, and hot- or cold-big-bang islands found no passage establishing the cited identification; the uncertainty about whether the islands connect is the citing authors’ own statement. (LLM, conf=0.72)

    Experimental — accuracy not yet measured

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Cites

Flagged first, then by citations

Research works printed but not linked: 3

  1. Albrecht, F. Occionero (Berlin : Springer)
  2. W. H., & Schechter, P. 1974, ApJ, 187, Press, 425
  3. Smoot, L1 M. 1998, preprint (gr-qc/9704009) · arXiv

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Related

Authors
Tegmark, M., & Rees, M. J.
Affiliations
  • Institute for Advanced Study (US)
  • University of Cambridge (GB)
ORCID
Venue
The Astrophysical Journal
Publisher
American Astronomical Society
Published
1998-06
Volume
499
Issue
2
Pages
526-532
ISSN
  • 0004-637X (ISSN-L)
  • 1538-4357
DOI
10.1086/305673
OpenAlex
W2038698427
Cited by
159
References
45
Citations by year
2026: 2 · 2025: 3 · 2023: 1 · 2022: 4 · 2021: 2 · 2020: 1 · 2019: 4 · 2018: 4 · 2017: 3 · 2016: 15 · 2015: 5 · 2013: 4 · 2012: 9
FWCI
3.54
Type
journal article
Language
en
Open access
Locations
  • The Astrophysical Journal (publishedVersion)
  • arXiv (Cornell University) (acceptedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • National Aeronautics and Space Administration (NAS 526555, 526555)
  • Space Telescope Science Institute (NAS5- 26555, 5-26555, 26555)
Topics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Galaxies: Formation, Evolution, Phenomena
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Dark Matter and Cosmic Phenomena
Keywords
cosmic microwave background anisotropies, density fluctuation amplitude, anthropic principle, cosmological constant, cosmic curvature, supermassive black holes, galaxy formation, star formation, supernova nucleosynthesis, inflation (cosmology), cosmic defects, fundamental physical constants, habitability

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