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Before cosmic reionization, hydrogen atoms acquire a spin polarizationquadrupole through interaction with the anisotropic 21-cm radiation field. Theinteraction of this quadrupole with anisotropies in the cosmic microwavebackground (CMB) radiation field gives a net spin orientation to the hydrogenatoms. The 21-cm radiation emitted by these spin-oriented hydrogen atoms iscircularly polarized. Here, we reformulate succinctly the derivation of theexpression for this circular polarization in terms of Cartesian (rather thanspherical) tensors. We then compute the angular power spectrum of the observedStokes-$V$ parameter in the standard $\Lambda$CDM cosmological model and showhow it depends on redshift, or equivalently, the observed frequency.

Standard Model Prediction for Cosmological 21cm Circular Polarization