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arXiv · 2603.12444

Stress-Energy Tensor of a Scalar Field on a Product Spacetime with a Time-Dependent Compact Dimension

Anamitra Paul·Sonia Paban
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Abstract

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 ($\mathcal{M}^{1, \,d-1} \times \mathcal{S}^1$), 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.

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Anamitra Paul, Sonia Paban. 2026-03-12. Stress-Energy Tensor of a Scalar Field on a Product Spacetime with a Time-Dependent Compact Dimension. https://arxiv.org/abs/2603.12444

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