Reconstruction of the primordial power spectra with Planck and BICEP2
  By using the cubic spline interpolation method, we reconstruct the shape of
the primordial scalar and tensor power spectra from the recently released {\it
Planck} temperature and BICEP2 polarization cosmic microwave background data.
We find that the vanishing scalar index running ($\dd n_s/\dd\ln k$) model is
strongly disfavored at more than $3\sigma$ confidence level on the $k=0.0002$
Mpc$^{-1}$ scale. Furthermore, the power-law parameterization gives a blue-tilt
tensor spectrum, no matter using only the first 5 bandpowers $n_t =
1.20^{+0.56}_{-0.64} (95% {\rm CL})$ or the full 9 bandpowers $n_t =
1.24^{+0.51}_{-0.58} (95% {\rm CL})$ of BICEP2 data sets. Unlike the large
tensor-to-scalar ratio value ($r\sim0.20$) under the scale-invariant tensor
spectrum assumption, our interpolation approach gives $r_{0.002} < 0.060 (95%
{\rm CL})$ by using the first 5 bandpowers of BICEP2 data. After comparing the
results with/without BICEP2 data, we find that {\it Planck} temperature with
small tensor amplitude signals and BICEP2 polarization data with large tensor
amplitude signals dominate the tensor spectrum reconstruction on the large and
small scales, respectively. Hence, the resulting blue tensor tilt actually
reflects the tension between {\it Planck} and BICEP2 data.
