Abstract
Assuming a toroidal space with finite volume, we derive analytically the full one-loop vacuum energy for a scalar field tunnelling between two degenerate vacua, taking into account discrete momentum. The Casimir energy is computed for an arbitrary number of dimensions using the Abel-Plana formula, while the one-loop instanton functional determinant is evaluated using the Green’s functions for the fluctuation operators. The resulting energetic properties are non-trivial: both the Casimir effect and tunnelling contribute to the Null Energy Condition violation, arising from a non-extensive true vacuum energy. We discuss the relevance of this mechanism to induce a cosmic bounce, requiring no modified gravity or exotic matter.
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Acknowledgments
The work of W.Y.A. and J.A. is supported by the Engineering and Physical Sciences Research Council (grant No. EP/V002821/1). The work of J.A. and S.P. is supported by the Leverhulme Trust (grant No. RPG-2021-299). J.A. is also supported by the Science and Technology Facilities Council (grant No. STFC-ST/X000753/1). For the purpose of Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission.
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Ai, WY., Alexandre, J., Carosi, M. et al. Double-well instantons in finite volume. J. High Energ. Phys. 2024, 99 (2024). https://doi.org/10.1007/JHEP05(2024)099
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DOI: https://doi.org/10.1007/JHEP05(2024)099