Layered Gravity and Layered Cosmology: A Minimal Oscillatory Extension of General Relativity with Testable Predictions

This work develops the cosmological sector of Layered Gravity Theory (LGT), showing that a periodic, layered microstructure in the gravitational coupling produces small but physically meaningful oscillatory features in the cosmic expansion history. Unlike standard scalar–tensor models, LGT generates controlled, non-singular oscillations in H(z), transient acceleration episodes, and phase‑dependent deviations in early‑ and late‑time cosmology—all while remaining fully consistent with gravitational‑wave propagation constraints, solar‑system tests, and CMB background measurements. Starting from the covariant LGT action, we derive the modified Friedmann equations and demonstrate that the layered scalar field naturally yields homogeneous oscillatory solutions. These solutions modulate the effective Planck mass and induce wiggles in the Hubble rate without introducing ghosts, tachyons, or gradient instabilities. The theory reduces smoothly to GR when the modulation parameters vanish, ensuring observational viability. A key result is that the cosmological sector inherits the full BRST consistency of LGT: the constraint algebra closes, the BRST charge remains nilpotent, and the physical spectrum contains only three propagating degrees of freedom. This establishes LGT cosmology as a quantum‑consistent extension of GR capable of producing novel, testable signatures in precision cosmology. The oscillatory structure identified here provides a new phenomenological window into cosmic expansion and offers a concrete alternative to dark‑energy parametrizations that rely on monotonic deviations from GR. LGT cosmology predicts distinctive phase‑dependent features that upcoming surveys—Euclid, LSST, SKA—could directly probe.