Dark energy with oscillatory tracking potential: Observational
  Constraints and Perturbative effects
  The cosmological models exhibiting tracker properties have great significance
in the context of dark energy as they can reach the present value of dark
energy density from a wide range of initial conditions, thereby alleviating
both the fine-tuning and the cosmic coincidence problem. The
$\alpha$-attractors, which are originally discussed in the context of
inflation, can exhibit the properties of dark energy as they can behave like
cosmological trackers at early times and show the late time behaviour of a
cosmological constant. In the present paper, we study the Oscillatory Tracker
Model (OTM), which belongs to the family of $\alpha$-attractor dark energy
models. Using the current observational data sets like Cosmic Microwave
Background (CMB), Baryon Acoustic Oscillation (BAO) and type 1a supernova data
(Pantheon compilation), we constrain the parameters of the model and estimate
both the mean and best-fit values. Although the oscillatory tracker model
contains a larger set of parameters than the usual LCDM model, the common set
of parameters of both agree within $1\, \sigma$ error limits. Our observations
using both high redshift and low redshift data supports Hubble parameter value
$H_0 = 67.4$ Kms$^{-1}$Mpc$^{-1}$. We study the effect of the OTM on the CMB
temperature and polarization power spectra, matter power spectrum and $f
\sigma_8$. Our analysis of the CMB power spectrum and matter power spectrum
suggests that the oscillatory tracker dark energy model has noticeable
differences from usual LCDM predictions. Yet, in most cases, the agreement is
very close.
