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.

3 pages, no figure

References in corpus (6)

• Imprints of anisotropic inflation on the cosmic microwave background
• Anisotropic Inflation from Charged Scalar Fields
• Suppressing the impact of a high tensor-to-scalar ratio on the temperature anisotropies
• On quantifying and resolving the BICEP2/Planck tension over gravitational waves
• Scalar-tensor correlations and large-scale power suppression
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Cited by in corpus (5)

• The TT, TB, EB and BB correlations in anisotropic inflation
• Statistical Anisotropies in Gravitational Waves in Solid Inflation
• Hemispherical asymmetry from an isotropy violating stochastic gravitational wave background
• D-Flation
• Naturally large tensor-to-scalar ratio in inflation