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 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.
Keywords
Cite
@article{arxiv.1404.5112,
title = {Scalar-Tensor Anti-Cross-Correlation does not Help to Reconcile the Tension between BICEP2 and Planck},
author = {Razieh Emami and Hassan Firouzjahi and Yi Wang},
journal= {arXiv preprint arXiv:1404.5112},
year = {2014}
}
Comments
3 pages, no figure