Observational Constraints on Quintessence: Thawing, Tracker, and Scaling
  models
  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, Cosmic Microwave Background, and Baryon Acoustic Oscillations. 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 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 LCDM.
