Odd-parity bipolar spherical harmonics
Bipolar spherical harmonics (BiPoSHs) provide a general formalism for quantifying departures in the cosmic microwave background (CMB) from statistical isotropy and from Gaussianity. However, prior work has focused only on BiPoSHs with even parity. Here we show that there is another set of BiPoSHs with odd parity, and we explore their cosmological applications. We describe systematic artifacts in a CMB map that could be sought by measurement of these odd-parity BiPoSH modes. These BiPoSH modes may also be produced cosmologically through lensing by gravitational waves (GWs), among other sources. We derive expressions for the BiPoSH modes induced by the weak lensing of both scalar and tensor perturbations. We then investigate the possibility of detecting parity-breaking physics, such as chiral GWs, by cross-correlating opposite-parity BiPoSH modes with multipole moments of the CMB polarization. We find that the expected signal-to-noise of such a detection is modest.
Additional Information© 2012 American Physical Society. Received 15 September 2011; published 25 January 2012. L. G. B. thanks Esfandiar Alizadeh, Christopher Hirata and Fabian Schmidt for useful discussions, and acknowledges the support of the NSF. M.K. thanks the support of the Miller Institute for Basic Research in Science and the hospitality of the Department of Physics at the University of California, Berkeley, where part of this work was completed. This work was supported at Caltech by DoE DE-FG03-92-ER40701, NASA NNX10AD04G, and the Gordon and Betty Moore Foundation. T. S. acknowledges support from Swarnajayanti grant, DST, India and the visit to Caltech during which the work was carried out.
Published - PhysRevD.85.023010.pdf