We invoke the constraints imposed on currently viable inflationary dar
k matter models by the abundance of quasars at all redshifts. A simple
model for the evolution of the number density of quasars is developed
by assuming that the host galaxies form at peaks of the linear densit
y field. Short quasar lifetimes (t(Q) is similar to 10(7)-10(8) yr) co
rresponding to quasars radiating at the Eddington limit are required i
n order to account for the abundance and number evolution of quasars.
Only if the quasar lifetime is approximately 10(7) yr can the tilted C
DM model, with n is similar to 0.7, the scaled (OMEGA(CDM) + OMEGA(A)
= 1) CDM model, and the (OMEGA(CDM) = 0.7, OMEGA(nu) = 0.3) mixed mode
l, all account for the observed quasar abundance at high redshift.