  We discuss several approaches to determine the Casimir force in inertial
frames of reference in different dimensions. On an example of a simple model
involving mirrors in Rindler spacetime we show that Casimir's and Lifschitz's
methods are inequivalent and only latter can be generalized to other spacetime
geometries. For conformally coupled fields we derive the Casimir force in
conformally flat spacetimes utilizing an anomaly and provide explicit examples
in the Friedmann-Lemaitre-Robertson-Walker $(k=0)$ models.
