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 CMB. We show that unlike the Zeeman effect, where $M_F=\pm 1$ have opposite energy shifts, the CMB quadrupole shifts $M_F=\pm 1$ 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.

20 pages, significantly expanded description of the effect; matches PRD accepted version

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Cited by in corpus (11)

• Constraining primordial black holes as dark matter using the global 21-cm signal with X-ray heating and excess radio background
• Heating of the intergalactic medium by the cosmic microwave background during cosmic dawn
• Polarized Redundant-Baseline Calibration for 21 cm Cosmology Without Adding Spectral Structure
• Exploring circular polarization in the CMB due to conventional sources of cosmic birefringence
• Lyman-$\alpha$ Polarization Intensity Mapping
• Physics Beyond The Standard Model with Circular Polarization in the CMB and CMB-21cm Cross-Correlation
• Ionospheric Attenuation of Polarized Foregrounds in 21 cm Epoch of Reionization Measurements: A Demonstration for the HERA Experiment
• Polarisation of high energy gamma-rays after scattering
• A Multi-messenger view of Cosmic Dawn: Conquering the Final Frontier
• Linear Polarization of the 21 cm Line from the Epoch of Reionization
• Standard Model Prediction for Cosmological 21cm Circular Polarization