  We present a realistic scenario of tracking of scalar fields with varying
equation of state. The astrophysical constraints on the evolution of scalar
fields in the physical universe are discussed. The nucleosynthesis and the
galaxy formation constraints have been used to put limits on $\Omega_\phi$ and
estimate $\epsilon$ during cosmic evolution. Interpolation techniques have been
applied to estimate $\epsilon\simeq0.772$ at the present epoch. The epoch of
transition from matter to quintessence dominated era and consequent onset of
acceleration in cosmic expansion is calculated and taking the lower limit
$\Omega_n^0 = 0.2$ as estimated from $SN_e I_a$ data, it is shown that the
supernova observations beyond redshift $z=1$ would reveal deceleration in
cosmic expansion.
