Since an acceptable dark matter candidate may interact only weakly with ord
inary matter and radiation, it is of interest to consider the limiting case
where the dark matter interacts only with gravity and itself, the matter o
riginating by the gravitational particle production at the end of inflation
. We use the bounds on the present dark mass density and the measured large
-scale fluctuations in the thermal cosmic background radiation to constrain
the two parameters in a self-interaction potential that is a sum of quadra
tic and quartic terms in a single scalar dark matter field that is minimall
y coupled to gravity. In quintessential inflation, where the temperature at
the end of inflation is relatively low, the field starts acting like cold
dark matter relatively late, shortly before the epoch of equal mass densiti
es in matter and radiation. This could have observable consequences for gal
axy formation. We respond to recent criticisms of the quintessential inflat
ion scenario, since these issues also apply to elements of the noninteracti
ng dark matter picture. [S0556-2821(99)08518-5].