Stress-energy tensor of a scalar field on a product spacetime with a time-dependent compact dimension

A bstract We compute the vacuum expectation value of the stress-energy tensor of a scalar field on a product spacetime composed of an FLRW background times a compact dimension (ℳ 1, d− 1 × 𝒮 1 ), where the size of the latter is allowed to vary with time. We modify the standard adiabatic regularization prescription to obtain analytic expressions for both d = 3 and d = 4. In the massless and conformally coupled limit, the leading order time-dependent results are consistent with known time-independent Casimir contributions. Furthermore, in this limit, the higher-order time-dependent corrections, when the FLRW and compact-dimension scale factors coincide, match known results for (1 + d )-dimensional FLRW spacetime.