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

The apparent discrepancy between the value of the tensor-to-scalar ratio reported by the BICEP2 collaboration, $r = 0.20^{+0.07}_{-0.05}$ 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 $k_* = 0.05$ Mpc$^{-1}$, assuming $n_t = 0$, whereas the Planck limit was provided at $k_* = 0.002$ 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 $k_* = 0.05$ 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 $r = 0.16^{+0.06}_{-0.05}$ and the discrepancy becomes of order $1.3σ$ only.

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