  A brief account of the current cosmological observations is given and their
implications for QCDM and $\Lambda$CDM cosmologies are discussed. The
nucleosynthesis and the galaxy formation constraints have been used to put
limits on $\Omega_\phi$ during cosmic evolution, and develop a realistic
approach to the tracking behaviour of quintessence fields. The astrophysical
constraints are applied to interpolate the value of the tracking parameter
$\epsilon \simeq 0.75$ at the present epoch and also to find the lower and the
upper limits for $\Lambda$ in the accelerating universe. It is shown that the
transition from deceleration to acceleration in the cosmic expansion occurs
earlier in $\Lambda$CDM cosmology compared to QCDM cosmology.
