The no-boundary reality lock is a causality lock: no causal dispersion, dissipative or not, can break the fluctuation antisymmetry
Abstract
The Lorentzian no-boundary path integral predicts unsuppressed cosmological fluctuations— the Feldbrugge–Lehners–Turok (FLT) catastrophe. A companion paper established a conjugate reality lock: because the minisuperspace action has real parameters, conjugate saddles carry exactly antisymmetric fluctuation exponents, so no real perturbation-sector modification can render both members of a pair suppressed. That result left one physical escape open in principle—a reality-breaking modification, such as the dissipative Beliaev decay of phonons in a Bose–Einstein-condensate (BEC) analogue, whose k5linewidth is a genuine laboratory-observable (Appendix A). Here we close that escape. We prove that the antisymmetry Re G(N¯) = − Re G(N) survives for any dispersion self-energy Σ that is hermitian-analytic, Σ(¯z) = Σ(z), provided the on-shell frequency contour does not cross the cut of Σ. Reality is not what the lock requires; hermitian analyticity is. A retarded, Kramers–Kronig self-energy— any causal one—is hermitian-analytic by construction, so physical dissipation cannot break the lock; only an acausal term can, and acausal terms are not physics. The proof is a two-line Riccati argument, and we confirm it numerically using the exact causal self-energy of the Beliaev absorptive part ρ(ω) ∝ ω5, built in closed form from the plasma-dispersion (Faddeeva) function: the causal self-energy preserves the antisymmetry to ∼10−8 and cutoff-independently,whereas the same absorptive part without its Kramers–Kronig real partner breaks it at O(1). The obstruction of the companion paper thus strengthens from reality to causality: the FLT catastrophe is protected against the entire class of causal dispersive modifications.
Fields of Study & Subjects
Quantum Electrodynamics and Casimir Effect
Noncommutative and Quantum Gravity Theories
Cosmology and Gravitation Theories
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 13 July 2026
- Language
- EN
- Document type
- Preprint