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We examine the recent proposal [1] that the anti-cross-correlation of thescalar and tensor primordial fluctuations reconciles the tension between BICEP2and Planck observations. We show that unfortunately the contribution from thescalar-tensor correlation to the CMB temperature power spectrum vanishes oncesummed 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-weightedspherical harmonics when projecting fields with nonzero spins into the CMB sky.These nonzero spin-weighted spherical harmonics are subject to orthogonalityconditions when summed over the angular direction and thus the desiredcross-correlation between the scalar and tensor perturbations in CMB mapvanishes.

Scalar-Tensor Anti-Cross-Correlation does not Help to Reconcile the Tension between BICEP2 and Planck