Emission-angle and polarization-rotation effects in the lensed CMB
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Publication Date
2017-08Journal Title
Journal of Cosmology and Astroparticle Physics
ISSN
1475-7516
Publisher
IOP Publishing
Type
Article
This Version
AM
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Lewis, A., Hall, A., & Challinor, A. (2017). Emission-angle and polarization-rotation effects in the lensed CMB. Journal of Cosmology and Astroparticle Physics https://doi.org/10.1088/1475-7516/2017/08/023
Abstract
Lensing of the CMB is an important effect, and is usually modelled by remapping the unlensed CMB fields by a lensing deflection. However the lensing deflections also change the photon path so that the emission angle is no longer orthogonal to the background last-scattering surface. We give the first calculation of the emission-angle corrections to the standard lensing approximation from dipole (Doppler) sources for temperature and quadrupole sources for temperature and polarization. We show that while the corrections are negligible for the temperature and E-mode polarization, additional large-scale B-modes are produced with a white spectrum that dominates those from post-Born field rotation (curl lensing). On large scales about one percent of the total lensing-induced B-mode amplitude is expected to be due to this effect. However, the photon emission angle does remain orthogonal to the perturbed last-scattering surface due to time delay, and half of the large-scale emission-angle B modes cancel with B modes from time delay to give a total contribution of about half a percent. While not important for planned observations, the signal could ultimately limit the ability of delensing to reveal low amplitudes of primordial gravitational waves. We also derive the rotation of polarization due to multiple deflections between emission and observation. The rotation angle is of quadratic order in the deflection angle, and hence negligibly small: polarization typically rotates by less than an arcsecond, orders of magnitude less than a small-scale image rotates due to post-Born field rotation (which is quadratic in the shear). The field-rotation B modes dominate the other effects on small scales.
Keywords
CMBR theory, gravitational lensing, CMBR polarisation, gravitational waves, CMBR polarization
Sponsorship
AL acknowledges support from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement No. [616170], and AL and AC from the Science and Technology Facilities Council [grant numbers ST/L000652/1 and ST/N000927/1, respectively]. AH is supported by a United Kingdom Space Agency Euclid grant, and an STFC Consolidated Grant.
Funder references
Science and Technology Facilities Council (ST/N000927/1)
Identifiers
External DOI: https://doi.org/10.1088/1475-7516/2017/08/023
This record's URL: https://www.repository.cam.ac.uk/handle/1810/267339
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