Reconstruction of initial Asymptotic-de Sitter mode in light of the
  Planck data
  The recently relased \emph{Planck} data, emphasize that the background
geometry of inflation is not pure de Sitter, but from the slow variation of
Hubble parameter during the inflationary era, it can be quasi-de Sitter. This
motivates us to consider an asymptotic de Sitter mode function for
reconstruction of initial mode and primordial power spectrum of curvature
perturbation. Using Markov Chain Monte Carlo (MCMC) method together with
applying recent observational constraints from the Cosmic Microwave Background
(CMB) data for our parametrized asymptotic initial mode shows some deviation
from pure de Sitter or Bunch-Davies mode. Based on \emph{Planck 2015} data
release the amplitude of scalar perturbations in $ 68 \%$ confidence level is
$10^{9} A_s =2.77^{+0.32}_{-0.35}$ and deviation from Bunch-Davies mode is
$\sim 0.03-0.04$. In this parametrization, the CMB power spectrum of our model
shows more red-tilt in comparison with $\Lambda \rm{CDM}$ model. Furthermore,
we found upper limit for tensor-to-scalar ratio with different pivot scales
$r_{0.05}< 0.0272$ and $ r_{0.002}< 0.0242$.
