Anomalous Casimir effect in axion electrodynamics

We study the Casimir effect in axion electrodynamics. A finite \(\theta\)-term affects the energy dispersion relation of photon if \(\theta\) is time and/or space dependent. We focus on a special case with linearly inhomogeneous \(\theta\) along the \(z\)-axis. Then we demonstrate that the Casimir force between two parallel plates perpendicular to the \(z\)-axis can be either attractive or repulsive, dependent on the gradient of \(\theta\). We call this repulsive component in the Casimir force induced by inhomogeneous \(\theta\) the anomalous Casimir effect.