Layered Gravity: A Periodic Scalar–Tensor Theory with Quantum Consistency and Ultraviolet Completion

This work develops Layered Gravity Theory (LGT), a scalar–tensor extension of General Relativity featuring a periodic nonminimal coupling and an exponentially damped oscillatory scalar profile. These structures generate smooth, controlled deviations from GR in strong‑field regimes while preserving all current weak‑field constraints, including solar‑system tests, laboratory inverse‑square‑law experiments, and multimessenger bounds from GW170817. We derive the full covariant field equations, analyze the weak‑field limit, and show that the layered microstructure produces characteristic oscillatory corrections in the redshift and timing signatures of neutron stars and stellar‑mass black holes. In cosmology, the periodic coupling induces small oscillatory features in the expansion history and allows transient acceleration without a cosmological constant. A central result is the nonperturbative BRST formulation of LGT. We construct the complete constraint algebra, verify BRST nilpotency, and compute the one‑loop effective action using heat‑kernel techniques. The relevant Seeley–DeWitt coefficients remain smooth on layered backgrounds, and no local BRST anomaly arises, demonstrating quantum consistency at one loop. We further show that the layered microstructure can originate from ultraviolet physics. Three mutually independent UV completions—5D Kaluza–Klein reduction, axion embeddings with instanton‑generated periodicity, and periodic fixed points in functional renormalization‑group flows—naturally reproduce the LGT action in the infrared. These results establish LGT as a theoretically consistent, observationally viable, and ultravioletly motivated extension of scalar–tensor gravity.