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Coupling a pseudoscalar to $R\tilde R$ splits the two tensor helicities, so the primordial background is circularly polarised [@alexander2009; @alexander2006].
A pseudoscalar coupled to $F\tilde F$ amplifies one helicity of the gauge field, which in turn sources chiral tensors and parity-odd scalar correlators [@sorbo2011].
The scalar sector can carry parity violation only from the four-point function onwards [@shiraishi2016].