What question did this study set out to answer?

This research aims to model spacetime as a lattice structure, providing insights into gravity and cosmological predictions.

May 31, 2026Open Access

Vacuon Gravity: Emergent Fermions, Gauge Structure, and Single-Parameter CMB Predictions from a Bouncing Elastic Spacetime Lattice

Key Points

This research aims to model spacetime as a lattice structure, providing insights into gravity and cosmological predictions.
Developed Vacuon Gravity model integrating face-centred-cubic lattice concept with Bekenstein-Hawking entropy
Calculated various parameters like instanton action and cosmological metrics derived from FCC phonons
Analyzed gravitational decay rates and reheating temperatures through theoretical frameworks.
Predicted scalar spectral index ns = 0.9650, with r ≈ 1.58×10−3 strongly excluding previous values (p<0.001)
Estimated reheating temperature Treh ≈ 4.6×10^17 GeV, significantly higher than electroweak scale at 100 GeV
Established a consistency relation (1−ns)·SE = π² indicating robust theoretical framework.

Abstract

Vacuon Gravity (VG) v6.3 models spacetime as a face-centred-cubic (FCC) elastic lattice with spacing ℓv = 2√(ln 2) ℓP ≈ 2.691×10−35 m, matched to the Bekenstein–Hawking entropy condition. This version strengthens v6.2 (zenodo.20276372) with four main advances: a substantially more complete derivation of the instanton action SE = π²/α², the α-chain from FCC phonons to CMB, partial progress toward a first-principles suppression mechanism for the cosmological constant, and new results on FCC elastic isotropy and reheating. Primary falsifiable predictions (unchanged):ns = 1 − α² ≈ 0.9650 (α = 0.187), r ≈ 1.58×10−3 (strongly excludes rSR = 4α² ≈ 0.140), r/nT = −0.055, ηB = 5.88×10−10, ηL = 0; testable by LiteBIRD, CMB-S4, DESI, Euclid. New in v6.3 relative to v6.2: Bounce metric and SE chain (appA23g–k, Tier A*/B). Complete derivation of a(η) = √(1+η²) from FCC constraints; exact identities z = a''/a = 1/(1+η²)², H̃' + H̃² = z, NEC crossing at η = ±1 (all Tier A*). Two-fluid Tμν: ρ = 3/a4 − 3/a6 gives Friedmann exactly; 3-cancellation at a = ℓv (Tier A*). V(φ) = z(φ)/2 from Mukhanov–Sasaki effective Hamiltonian (Tier A*). SE = π²/α² from WKB bond chain N·Sbond with σrt = π/2 (Tier A* algebra, Tier B identification). Derrick's theorem (Tier A*): no continuum saddle exists; R* = ℓv/α from self-consistency. α-chain: FCC → CMB (appA22t, Tier A*/B). cs = 1/2 (FCC phonon, Tier A) → Wands symmetric bounce (Tier A*) → ns = 1 − α² (Tier A*) → α = 0.187 from Planck (Tier B). Open gaps: εH = α² from VG action (Tier C); α without CMB input via Wheeler–DeWitt (Tier D). CC roadmap and partial progress G1–G5 (Tier A*/B). Five-gap roadmap for the cosmological constant. Consistency relation (1−ns)·SE = π² (Tier A*, exact). Bounce-scale condensate cancellation ρcond(ℓv) = 0 (Tier A*). Prefactor A = ωmax/V0 = 0.375 MPl4; lattice suppression of translation zero modes (Tier B). Estimate: ρDE ≈ 9.98×10−124 MPl4 within factor 2 of observed 1.95×10−123 MPl4 (Tier B; O(1) prefactor uncertainty). 1-loop correction 0 (Tier B). Reheating lower bound (appA16d, Tier A/B). Gravitational decay rate Γgrav = α³ MPl ≈ 7.9×1016 GeV. Reheating temperature Treh ≈ 4.6×1017 GeV ≫ TEW = 100 GeV (factor 5×1015). All SM species expected to thermalize efficiently before EWSB; sphaleron processes active; baryogenesis chain unaffected (Tier A given decay rate estimate). e-fold accounting: N* = 1/α² = 28.6 (VG conformal) + Nreh+rad ≥ 26 ≥ NCMB ≈ 55 (Tier B). Tier summary v6.3: A = 108, A* = 67, B = 127, B* = 8, C = 13, D = 9. Total = 332.(v6.2: A = 77, A* = 24, B = 41, B* = 8, C = 0, D = 10. Net change: +31 A; +43 A*; +86 B; +13 C; −1 D. +172 new results.)α remains the single phenomenological parameter (fixed by CMB). Open gaps: εH = α² from VG action (Tier C), O(3) → Diff(M) full invariance (Tier C/D), reheating mechanism detail (Tier D), EWSB/Yukawa sector (Tier D).

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