Constraints on quintessence scalar field models using cosmological observations

We consider a variety of quintessence scalar field models in a homogeneous and isotropic geometry of the Universe with zero spatial curvature aiming to provide stringent constraints using a series of cosmological datasets, namely, the cosmic microwave background (CMB) observations, baryon acoustic oscillations (BAOs), joint light curve analysis (JLA) from supernovae type Ia, redshift space distortions (RSDs), and the cosmic chronometers (CCs). From the qualitative evolution of the models, we find that all of them are able to execute a fine transition from the past decelerating phase to the presently accelerating expansion where, in addition, the equation of state of the scalar field (also the effective equation of state) might be close to that of the ΛCDM cosmology depending on its free parameters. From the observational analyses, we find that the scalar field parameters are unconstrained irrespective of all the observational datasets. In fact, we find that the quintessence scalar field models are pretty much determined by the CMB observations, since any of the external datasets such as BAOs, JLA, RSDs, and CCs does not add any constraining power to the CMB. Additionally, we observe a strong negative correlation between the parameters H₀ (present value of the Hubble parameter) and Ωₘ₀ (density parameter for the matter sector, i.e., cold dark matter plus baryons) exists while no correlation between H₀ and σ₈ (amplitude of the matter fluctuation). We also comment that the present models are unable to reconcile the tension on H₀. Finally, we conclude our work with the Bayesian analyses which report that the noninteracting ΛCDM model is preferred over all the quintessence scalar field models.