Constraints over Cosmological Constant and Quintessence Fields in an Accelerating Universe

A brief account of the current cosmological observations is given and their implications for QCDM and $\mathrm{\Lambda }$CDM cosmologies are discussed. The nucleosynthesis and the galaxy formation constraints have been used to put limits on ${\mathrm{\Omega }}_{\varphi }$ 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 $ϵ\simeq 0.75$ at the present epoch and also to find the lower and the upper limits for $\mathrm{\Lambda }$ in the accelerating universe. It is shown that the transition from deceleration to acceleration in the cosmic expansion occurs earlier in $\mathrm{\Lambda }$CDM cosmology compared to QCDM cosmology.