Comparing the scalar-field dark energy models with recent observations
  We investigate the general properties of a class of scalar-field dark energy
models (i.e., $\phi$CDM models) which behave like cosmological trackers at
early times. Particularly, we choose three $\phi$CDM models with typical
potentials, i.e., $V(\phi)\propto \phi^{-\alpha}$ (inverse power-law (IPL)
model), $V(\phi)\propto \coth^{\alpha}{\phi}$ (L-model) and $V(\phi)\propto
\cosh(\alpha\phi)$ (Oscillatory tracker model), where the latter two models are
based on the $\alpha$-attractors originated from the study of inflation. These
models, which reduce to the $\Lambda$CDM model with $\alpha \to 0$, are studied
and compared with the recent observations, including the Pantheon sample of
type Ia supernovae (SNe Ia), baryon acoustic oscillations (BAO) measurements
extracted from 6dFGS, BOSS and eBOSS, as well as the temperature and
polarization anisotropy power spectra data of cosmic microwave background
radiation (CMB) from Planck 2018 results. The observational constraints from
the combining sample (SNe Ia + BAO + CMB) indicate that none of the three
$\phi$CDM models exclude the $\Lambda$CDM model at $68.3\%$ confidence level.
We find that the CMB anisotropy data have obvious advantages in constraining
the dark energy models compared with other cosmological probes, which is
particularly evident in the L-model. Furthermore, we apply the Bayesian
evidence to compare the $\phi$CDM models and the $\Lambda$CDM model with the
analysis of the combining sample. The concordance $\Lambda$CDM model is still
the most supported one. In addition, among the three $\phi$CDM models, the IPL
model is the most competitive one, while the L-model/Oscillatory tacker model
is moderately/strongly disfavored.
