Cross-Correlation of Cosmological Birefringence with CMB Temperature
  Theories for new particle and early-Universe physics abound with
pseudo-Nambu-Goldstone fields that arise when global symmetries are
spontaneously broken. The coupling of these fields to the Chern-Simons term of
electromagnetism may give rise to cosmological birefringence (CB), a
frequency-independent rotation of the linear polarization of photons as they
propagate over cosmological distances. Inhomogeneities in the CB-inducing field
may yield a rotation angle that varies across the sky. Here we note that such a
spatially-varying birefringence may be correlated with the cosmic microwave
background (CMB) temperature. We describe quintessence scenarios where this
cross-correlation exists and other scenarios where the scalar field is simply a
massless spectator field, in which case the cross-correlation does not exist.
We discuss how the cross-correlation between CB-rotation angle and CMB
temperature may be measured with CMB polarization. This measurement may improve
the sensitivity to the CB signal, and it can help discriminate between
different models of CB.
