Casimir effect in conformally flat spacetimes

TL;DR

This paper investigates the Casimir effect in conformally flat spacetimes, comparing different calculation methods and deriving explicit forces in cosmological models, highlighting the advantages of Lifschitz's approach.

Contribution

It demonstrates that Lifschitz's method can be generalized to various spacetime geometries and derives explicit Casimir forces in conformally flat cosmological models.

Findings

Lifschitz's method is more generalizable than Casimir's in curved spacetimes.

Explicit Casimir forces are derived for Friedmann-Lemaitre-Robertson-Walker models.

The paper clarifies the applicability of different approaches to the Casimir effect in curved backgrounds.

Abstract

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.