A note of clarification: BICEP2 and Planck are not in tension

Abstract

The apparent discrepancy between the value of the tensor-to-scalar ratio reported by the BICEP2 collaboration, $r=0.20_{-0.05}^{+0.07}$ at 68% CL, and the Planck upper limit, $r<0.11$ at 95% CL, has attracted a great deal of attention. In this short note, we show that this discrepancy is mainly due to an `apples to oranges' comparison. The result reported by BICEP2 was measured at a pivot scale $k_{\ast }=0.05$ Mpc${}^{-1}$, assuming $n_t=0$, whereas the Planck limit was provided at $k_{\ast }=0.002$ Mpc${}^{-1}$, assuming the slow-roll consistency relation $n_t=-r/8$. One should obviously compare the BICEP2 and Planck results under the same circumstances. By imposing $n_t=0$, the Planck constraint at $k_{\ast }=0.05$ Mpc${}^{-1}$ becomes $r<0.135$ at $95$ CL, which can be compared directly with the BICEP2 result. Once a plausible dust contribution to the BICEP2 signal is taken into account (DDM2 model), $r$ is reduced to $r=0.16_{-0.05}^{+0.06}$ and the discrepancy becomes of order $1.3\sigma$ only.

Brief note (2 pages, 2 figures), just to clarify certain aspects about the comparison between the BICEP2 and Planck results

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