Quintessence is a canonical scalar field introduced to explain the late-time cosmic acceleration .
The cosmological dynamics of quintessence is reviewed , paying particular attention to the evolution of the dark energy equation of state w .
For the field potentials having tracking and thawing properties , the evolution of w can be known analytically in terms of a few model parameters .
Using the analytic expression of w , we constrain quintessence models from the observations of supernovae type Ia , cosmic microwave background , and baryon acoustic oscillations .
The tracking freezing models are hardly distinguishable from the \Lambda -Cold-Dark-Matter ( \Lambda CDM ) model , whereas in thawing models the today ’ s field equation of state is constrained to be w _ { 0 } < -0.7 ( 95 % CL ) .
We also derive an analytic formula for the growth rate of matter density perturbations in dynamical dark energy models , which allows a possibility to put further bounds on w from the measurement of redshift-space distortions in the galaxy power spectrum .
Finally we review particle physics models of quintessence–such as those motivated by supersymmetric theories .
The field potentials of thawing models based on a pseudo-Nambu-Goldstone boson or on extended supergravity theories have a nice property that a tiny mass of quintessence can be protected against radiative corrections .