Constraints on the small scale curvature perturbation using Planck-2015
  data
  The particles emitted from PBHs through the Hawking radiation have
interactions with the particles present in the Universe. Due to the
interactions, the evolution of the intergalactic medium (IGM) is changed and
the changes have imprints on the anisotropies of the cosmic microwave
background (CMB). In this paper, we focus on the PBHs with the lifetime in the
range of $10^{13}s \lesssim \tau_{\rm PBH} \lesssim 10^{17}s$, corresponding to
the mass range of $2.8\times 10^{13}\mathrm{g} \lesssim M_{\mathrm{PBH}}
\lesssim 2.5\times 10^{14}\mathrm{g}$. We update the constraints on the initial
mass fraction of PBHs using the Plank-2015 data. We find that the optimistic
upper limits are $4\times 10^{-29}\lesssim \beta(M_{\mathrm{PBH}}) \lesssim
5\times 10^{-28}$, depending on the mass of PBH. The formation of PBHs is
related to the primordial curvature perturbations. Therefore, using the
constraints on the initial mass fraction of PBHs, we get the upper limits on
the power spectrum of primordial curvature perturbation. For the investigated
mass range of PBHs, corresponding to the range of scales $8.9 \times 10^{15}\
\mathrm{Mpc^{-1}}\lesssim k \lesssim 2.8 \times 10^{16}\ \mathrm{Mpc^{-1}}$, we
find that the upper limits change slightly with a value of
$\mathcal{P}_\mathcal{R}(k) \sim 0.0045$, and the limits are slightly stronger
compared with the previous results.
