Constraints on quintessence scalar field models using cosmological
  observations
  We consider a varieties 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 data sets, namely,
the cosmic microwave background observations (CMB), baryon acoustic
oscillations (BAO), joint light curve analysis (JLA) from supernovae type Ia,
redshift space distortions (RSD), and the cosmic chronometers (CC). From the
qualitative evolution of the models, we find 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 $\Lambda$CDM
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 BAO, JLA, RSD, CC does not add any constraining power
to CMB. Additionally, we observe a strong negative correlation between the
parameters $H_0$ (present value of the Hubble parameter), $\Omega_{m0}$
(density parameter for the matter sector, i.e., cold dark matter plus baryons)
exists, while no correlation between $H_0$, and $\sigma_8$ (amplitude of the
matter fluctuation) are not correlated. We also comment that the present models
are unable to reconcile the tension on $H_0$. Finally, we conclude our work
with the Bayesian analyses which report that the non-interacting $\Lambda$CDM
model is preferred over all the quintessence scalar field models.
