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.