Planck Satellite Constraints on Pseudo-Nambu--Goldstone Boson
  Quintessence
  The Pseudo-Nambu-Goldstone Boson (PNGB) potential, defined through the
amplitude $M^4$ and width $f$ of its characteristic potential $V(\phi) = M^4[1
+ \cos(\phi/f)]$, is one of the best-suited models for the study of thawing
quintessence. We analyze its present observational constraints by direct
numerical solution of the scalar field equation of motion. Observational bounds
are obtained using Supernovae data, cosmic microwave background temperature,
polarization and lensing data from {\it Planck}, direct Hubble constant
constraints, and baryon acoustic oscillations data. We find the parameter
ranges for which PNGB quintessence gives a viable theory for dark energy. This
exact approach is contrasted with the use of an approximate equation-of-state
parametrization for thawing theories. We also discuss other possible
parameterization choices, as well as commenting on the accuracy of the
constraints imposed by {\it Planck} alone. Overall our analysis highlights a
significant prior dependence to the outcome coming from the choice of modelling
methodology, which current data are not sufficient to override.
