Perturbations in a scalar field model with virtues of $\Lambda$CDM

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.