  In the era of precision cosmology, the cosmological constant $\Lambda$ gives
quite an accurate description of the evolution of the Universe, but it is still
plagued with the fine-tuning problem and the cosmic coincidence problem. In
this work, we investigate the perturbations in a scalar field model that drives
the recent acceleration in a similar fashion that the cosmological constant
does and has the dark energy (DE) density comparable to the dark matter (DM)
energy density at the recent epoch starting from arbitrary initial conditions.
The perturbations show that this model, though it keeps the virtues of a
$\Lambda$CDM model, has a distinctive qualitative feature, particularly it
reduces the amplitude of the matter power spectrum on a scale of $8 h^{-1}\,
\mbox{Mpc}$, $\sigma_{8}$ at the present epoch.
