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

Abstract

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.

arXiv comment3 pages, no figure

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• Hemispherical asymmetry from an isotropy violating stochastic gravitational wave background
• D-Flation
• \bf $\delta M$ Formalism and Anisotropic Chaotic Inflation Power Spectrum
• Naturally large tensor-to-scalar ratio in inflation