Odd-parity cosmic microwave background bispectrum

Measurement of the CMB bispectrum, or three-point correlation function, has now become one of the principle efforts in early-Universe cosmology. Here we show that there is an odd-parity component of the CMB bispectrum that has been hitherto unexplored. We argue that odd-parity temperature-polarization bispectra can arise, in principle, through weak lensing of the CMB by chiral gravitational waves or through cosmological birefringence, although the signals will be small even in the best-case scenarios. Measurement of these bispectra requires only modest modifications to the usual data-analysis algorithms. They may be useful as a consistency test in searches for the usual bispectrum and to search for surprises in the data.