Double-well instantons in finite volume

Wen Yuan Ai, Jean Alexandre, Matthias Carosi, Björn Garbrecht, Silvia Pla

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number99
JournalJournal of High Energy Physics
Issue number5
StatePublished - May 2024


  • Cosmological models
  • Early Universe Particle Physics
  • Nonperturbative Effects
  • Solitons Monopoles and Instantons


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