Detecting primordial gravitational waves with circular polarization of the redshifted 21 cm line. I. Formalism
Abstract
We propose a new method to measure the tensor-to-scalar ratio r using the circular polarization of the 21 cm radiation from the pre-reionization epoch. Our method relies on the splitting of the F = 1 hyperfine level of neutral hydrogen due to the quadrupole moment of the cosmic microwave background (CMB). We show that unlike the Zeeman effect, where M_F = ± 1 have opposite energy shifts, the CMB quadrupole shifts M_F = ± 1 together relative to M_F = 0. This splitting leads to a small circular polarization of the emitted 21 cm radiation. In this paper (Paper I in a series on this effect), we present calculations on the microphysics behind this effect, accounting for all processes that affect the hyperfine transition. We conclude with an analytic formula for the circular polarization from the Dark Ages as a function of pre-reionization parameters and the value of the remote quadrupole of the CMB. We also calculate the splitting of the F = 1 hyperfine level due to other anisotropic radiation sources and show that they are not dominant. In a companion paper (Paper II) we make forecasts for measuring the tensor-to-scalar ratio r using future radio arrays.
Additional Information
© 2018 American Physical Society. (Received 9 August 2017; published 21 May 2018) We thank Vera Gluscevic and Antonija Oklopčić for enlightening conversations and comments during the preparation of this work. C. H. and A. M. are supported by the U.S. Department of Energy and the David & Lucile Packard Foundation. C. H. is supported by the Simons Foundation and the National Aeronautics and Space Administration. T. V. gratefully acknowledges support from the Schmidt Fellowship and the Fund for Memberships in Natural Sciences at the Institute for Advanced Study.Attached Files
Published - PhysRevD.97.103521.pdf
Accepted Version - 1707.03513
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Additional details
- Eprint ID
- 86527
- Resolver ID
- CaltechAUTHORS:20180521-153923564
- Department of Energy (DOE)
- David and Lucile Packard Foundation
- Simons Foundation
- NASA
- Schmidt Fellowship
- Institute for Advanced Study
- Created
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2018-05-21Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field
- Caltech groups
- TAPIR