← openxiv:gr-qc.2026.00004 · gr-qc
Solar system and laboratory tests of the spectral action scale
Explainer at the level of a researcher in an adjacent area. Read the original paper.
Assumes deep technical literacy. Bridges to the closest neighbouring fields.
**Problem statement:** The spectral action principle generates gravitational dynamics from the Dirac operator spectrum, introducing curvature-squared corrections with coefficients fixed by the Standard Model (SM) particle content. These corrections modify the graviton propagator and testable deviations from general relativity (GR) at short distances, but the observational viability of the spectral cutoff scale Λ remains unexplored. **Method:** Linearizing the spectral action around flat space and computing one-loop form factors for the SM yields dressed propagator denominators for spin-2 and spin-0 sectors. In the local Yukawa approximation, the static Newtonian potential acquires two exponential Yukawa terms with amplitudes (−4/3 and +1/3) determined solely by the spin decomposition, and ranges set by effective masses m₂ = Λ√(60/13) and m₀ = Λ/√[6(ξ−1/6)²]. The post-Newtonian parameter γ(r) is derived and confronted with seven gravitational experiments. **Main results:** The Newtonian 1/r singularity is regularized at short distances, and Newton’s law is recovered for r ≫ 1/Λ. The strongest bound comes from the Eöt-Wash torsion-balance experiment: Λ > 2.565×10⁻³ eV (95% CL), corresponding to a Yukawa range λ₁ < 36 μm and 1/Λ < 77 μm. All solar-system tests (Cassini, MESSENGER) are satisfied with exponential margin; Casimir and satellite experiments give no constraint. The bound varies by less than 8% across realistic Higgs couplings ξ, confirming dominance of the spin-2 channel. **Limitations:** The local Yukawa approximation neglects the full nonlocal form factors; the exact propagator yields a slightly shorter range, making the bound conservative. The β PPN parameter remains undetermined because nonlinear field equations are required. The massive spin-2 ghost mode (negative residue) raises interpretational questions (e.g., Lee–Wick or fakeon), unresolved here.
Explainers are best-effort summaries — they round corners. For the authoritative claims, read the paper itself.