  Most physical properties derived for quasars, as single entities or as a
population, depend upon the cosmology assumed. In this paper, we calculate the
quasar luminosity function and some related quantities for a flat universe
dominated by a cosmological constant $\Lambda$ ($\Lambda=0.9, \Omega=0.1$) and
compare them with those deduced for a flat universe with zero cosmological
constant ($\Lambda=0,\Omega=1$). We use the AAT quasar survey data (Boyle et
al. 1990) as input in both cases. The data are fit well by a pure luminosity
evolution model for both the cosmologies, but with different evolutionary
parameters. From the luminosity function, we predict (extrapolate) a greater
number of quasars at faint apparent magnitudes (twice the number at B=24, $z <
2.2$) for the $\Lambda$ dominated universe. This population of faint quasars at
high redshift would result in a higher incidence of gravitational lensing. The
total luminosity of the quasar population and the total mass tied up in black
hole remnants of quasars is not sensitive to the cosmology. However, for a
$\Lambda$ cosmology this mass is tied up in fewer but more massive black holes.

Astrophysics