We study the cross-correlation between the 21-cm and cosmic microwave background (CMB)
B
mode fluctuations which are induced by the cosmic birefringence when the nonconstant scalar field couples to the electromagnetic field strength. Such multiwavelength signals can potentially probe the reionization history of the Universe and also explore the nature of fundamental physics such as the parity violation and the scalar field dynamics in the early Universe. We illustrate the feasibility to detect such 21-cm-
B
mode cross-correlations through commonly discussed scalar field models, the quintessence-like scalar field which is responsible for the current dark energy and the axionlike scalar field which is responsible for the current dark matter density.
