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.
The Astrophysical Journal
- Pub Date:
- May 1998
- Cosmology: Theory;
- Cosmology: Large-Scale Structure of Universe;
- Revised to match accepted version. 8 pages, with 1 figure included. Color figure and related links at http://www.sns.ias.edu/~max/Q.html (faster from the US), from http://www.mpa-garching.mpg.de/~max/Q.html (faster from Europe) or from email@example.com. ApJ, in press