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Stress-Energy Tensor of a Scalar Field on a Product Spacetime with a Time-Dependent Compact Dimension
High Energy Physics - Theory · Submitted 12 Mar 2026 · Published version
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In the massless and conformally coupled limit, the leading order time-dependent results are consistent with known time-independent Casimir contributions.
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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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 0.98 | 0.94 | 0.11 | asserted 0.99 |
| s1 | We modify the standard adiabatic regularization prescription to obtain analytic expressions for both $d=3$ and $d=4$. | method 0.94 | 0.96 | 0.10 | asserted 1.00 |
| s2 | In the massless and conformally coupled limit, the leading order time-dependent results are consistent with known time-independent Casimir contributions. | result 0.87 | 0.80 | 0.17 | hedged possibility 0.76 |
| s3 | 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. | result 0.92 | 0.79 | 0.18 | asserted 0.97 |
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Original 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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What it cites · 3 sentences without a confident label
Uses data or values from 1 paper
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Atomic clock experiments constrain the current variation of the fine structure constant, $|α̇/α_0| < 10^-17 yr^-1$ [ref] , while ALMA measurements of absorption spectroscopy toward high-redshift quasars bound the variation $Δα= α(z=0.89)-α_0$ to $|Δα/α_0| < 0.55 p.p.m$ [ref] , which roughly translates to $|α̇/α_0| < 10^-16 yr^-1$, under the assumption of a constant rate.
2512.14441 · Introduction · 0.84
Compares with 1 paper
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[equation] The $0$-th order expressions, which may be interpreted as the Casimir energy/pressures, match known results for the time-independent case [ref] .
Quantum Horizons of the Standard Model Landscape · Scenario · 0.99
Cites as background 10 papers
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In cosmology, although quite a bit of work has been devoted to compactification dynamics (for examples, see [ref] ), we have found only one reference [ref] that has attempted to compute the time dependent corrections when gravity matters.
Dynamical compactification from de Sitter space · Introduction · 0.93
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In cosmology, although quite a bit of work has been devoted to compactification dynamics (for examples, see [ref] ), we have found only one reference [ref] that has attempted to compute the time dependent corrections when gravity matters.
2512.19793 · Introduction · 0.93
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In cosmology, although quite a bit of work has been devoted to compactification dynamics (for examples, see [ref] ), we have found only one reference [ref] that has attempted to compute the time dependent corrections when gravity matters.
Spontaneous decompactification · Introduction · 0.93
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