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.