For two types of quintessence models having thawing and tracking properties , there exist analytic solutions for the dark energy equation of state w expressed in terms of several free parameters .
We put observational bounds on the parameters in such scenarios by using the recent data of Supernovae type Ia ( SN Ia ) , Cosmic Microwave Background ( CMB ) , and Baryon Acoustic Oscillations ( BAO ) .
The observational constraints are quite different depending on whether or not the recent BAO data from BOSS are taken into account .
With the BOSS data the upper bounds of today ’ s values of w ( = w _ { 0 } ) in thawing models is very close to -1 , whereas without this data the values of w _ { 0 } away from -1 can be still allowed .
The tracker equation of state w _ { ( 0 ) } during the matter era is constrained to be w _ { ( 0 ) } < -0.949 at 95 % confidence level ( CL ) even without the BOSS data , so that the tracker models with w away from -1 are severely disfavored .
We also study observational constraints on scaling models in which w starts to evolve from 0 in the deep matter era and show that the transition to the equation of state close to w = -1 needs to occur at an early cosmological epoch .
In the three classes of quintessence models studied in this paper , the past evolution of the Hubble parameters in the best-fit models shows only less than the 2.5 % difference compared to the \Lambda CDM .