Why is the CMB fluctuation level 10^{-5}?

Abstract

We explore the qualitative changes that would occur if the amplitude Q ~ 10^{-5} of cosmological density fluctuations were different. If is less than about 10^{-6}, the cosmological objects that form would have so low virial temperatures that they may be unable to cool and form stars, and 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 is greater than about 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 Lambda would be invalid if both Q and Lambda could vary and there were no anthropic constraints on Q. The same applies to anthropic bounds on the curvature parameter Omega.