We explore the qualitative changes that would occur if the amplitude Q
similar to 10(-5) of cosmological density fluctuations were different
. If Q less than or similar to 10(-6), the cosmological objects that f
orm 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 retai
n the heavy elements necessary for planetary life. If Q greater than o
r similar to 10(-4), dense supermassive galaxies would form, and biolo
gical evolution could be marred by short disruption timescales for pla
netary orbits. If Q were still larger, most bound systems would collap
se 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 imp
lications for inflation and defect models and note that the recent ant
hropic upper bounds on the cosmological constant Lambda would be inval
id if both Q and Lambda could vary and there were no anthropic constra
ints on Q. The same applies to anthropic bounds on the curvature param
eter Omega.