Journal
PHYSICAL REVIEW D
Volume 90, Issue 2, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.90.021301
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Funding
- European Research Council (ERC STG) [279617]
- Stephen Hawking Advanced Fellowship
- Science and Technology Facilities Council [ST/L000636/1] Funding Source: researchfish
- STFC [ST/L000636/1] Funding Source: UKRI
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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.
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