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| Paper IPM / Physic / 13491 |
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We examine the recent proposal [1] that the anti-cross-correlation of the scalar and tensor primordial fluctuations reconciles the tension between BICEP2 and Planck observations. We show that unfortunately the contribution from the scalar-tensor correlation to the CMB temperature power spectrum vanishes once summed over the angular mode m so the tension between BICEP2 and Planck can not be reconciled. The reason is that one has to use the spin-weighted spherical harmonics when projecting fields with nonzero spins into the CMB sky. These nonzero spin-weighted spherical harmonics are subject to orthogonality conditions when summed over the angular direction and thus the desired cross-correlation between the scalar and tensor perturbations in CMB map vanishes.
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