  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.
