Scalar-tensor anticross-correlation does not help to reconcile the tension between BICEP2 and Planck

Abstract

We examine the recent proposal that the anticross-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 cosmic microwave background (CMB) temperature power spectrum vanishes once summed over the angular mode m so the tension between BICEP2 and Planck cannot 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. © 2014 American Physical Society.