← openxiv:gr-qc.2026.00004 · gr-qc
Solar system and laboratory tests of the spectral action scale
Explainer at the level of an undergraduate in the field. Read the original paper.
Assumes 1–2 courses of background. Domain terms may appear without definition.
The spectral action is a theoretical idea that generates gravity from the spectrum of a mathematical operator, introducing a new energy scale Λ. When applied to the Standard Model of particle physics, it predicts that Newton's law of gravity is modified at very short distances—roughly the scale 1/Λ. Instead of a simple 1/r force, the gravitational potential gains two additional Yukawa-type corrections, each with fixed strengths (amplitudes -4/3 and +1/3) that come from the spin properties of the graviton. The ranges of these corrections are set by Λ and the Higgs field's non-minimal coupling. This modified potential is finite at the origin (no more 1/r singularity) and returns to Newton's law at distances much larger than 1/Λ. To test this prediction, the authors compared the theory with seven experiments, including torsion balances, satellite time delays, Casimir force measurements, and lunar laser ranging. The strongest constraint comes from the Eöt-Wash torsion-balance experiment, which probes gravity at sub-millimeter scales. They found that Λ must be greater than about 2.565 × 10⁻³ electronvolts, meaning the modification range is shorter than about 77 micrometers. All solar-system tests (like Cassini's time delay) are easily satisfied because the corrections are exponentially tiny at astronomical distances. The bound depends only weakly on the Higgs coupling, making the result robust. This shows that the spectral action with Standard Model content passes all current gravitational tests, with future short-range experiments promising tighter limits.
Explainers are best-effort summaries — they round corners. For the authoritative claims, read the paper itself.