Electromagnetic waves propagating in the string axiverse

It is widely believed that axions are ubiquitous in string theory and could be dark matter. The peculiar features of axion dark matter are coherent oscillations and a coupling to the electromagnetic field through the Chern-Simons term. In this letter, we study the consequences of these two features of axions with mass in the range 10 eV to 10 eV. First, we study the parametric resonance of electromagnetic waves induced by the coherent oscillation of the axion. Since the resonance frequency is determined by the mass of the axion dark matter, if we detect this signal, we can get information on the mass of the axion dark matter. Second, we study the velocity of light in the background of the axion dark matter. In the presence of the Chern-Simons term, the dispersion relation is modified and the speed of light will oscillate in time. It turns out that the change in the speed of light would be difficult to observe. We argue that future radio wave observations of the resonance can give rise to a stronger constraint on the coupling constant and/or the density of the axion dark matter.