Vacuum Admissibility and Infrared Consistency in Emergent Gravity: A Gauge-Invariant Selection Framework with a Bunch–Davies Benchmark
Year: 2026
Type: preprint
Abstract: We develop a general methodology for testing the infrared admissibility of candidate reference states in emergent-gravity constructions. The central point is that vacuum selection by infrared consistency is an exclusion principle rather than, in general, a uniqueness theorem: a state may be ruled out in a specified physical channel if the final gauge-invariant gravitational response is non-integrable or otherwise singular, whereas passing such a test establishes admissibility only for the observable and channel examined. The framework separates exact zero modes from soft continuum modes and orders the analysis through canonical normalization, matched asymptotics, conserved-source reduction, gauge-invariant gravitational projection, Lorentzian reconstruction, spectral weighting, and the final observable-specificresponse integral. We formulate an abstract infrared-exponent propagation lemma that quantifies how singular or regular reconstruction maps can alter soft power counting and gives a sufficient integrability condition for the final response. For information-geometric models, the Bogoliubov–Kubo–Mori susceptibility enters as an optional initial module, not as a gravitational observable by itself. We then apply the framework to the Bunch–Davies sector of a massless minimally coupled scalar on four-dimensional de Sitter spacetime. Using the exact static-patch low-frequency normalization and horizon matching, the non-exceptional ℓ = 1 modes scale as O(√ω); the apparent 1/ω horizon-connection coefficient reconstructs the logarithmic static branch and does not yield an independent inverse-frequency divergence of the normalized mode. In the scalar-induced ℓ = 1 ⊗ ℓ = 1 → L = 2 channel, the quadratic matter source is O(Ω). We prove that the pure-dS4 homogeneous Kodama–Ishibashi operator has neither a zero mode nor a bounded threshold resonance and that the regular-origin/Jost Wronskian has a nonzero zero-frequency limit; hence the gravitational resolvent acquires no additional algebraic 1/Ω pole from the homogeneous threshold problem. The remaining global assumption is reduced to an explicit horizon-weighted bound on the fully projected source, together with the observable-specific Lorentzian pairing condition. Under these stated endpoint assumptions the conservative spectral weight is O(Ω4 ), so response kernels no more singular than 1/Ω are infrared integrable in this benchmark. The result is deliberately channel-specific and does not establish global stability or uniqueness of the Bunch–Davies state. The broader contribution is a reusable vacuum-admissibility protocol for emergent-gravity models in which the physical response map is specified.
Author: Margaritis, Iraklis
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213772527
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