The Resonant Nested Engine: A Cyclic Gravitational Cavity Model of Cosmology

We propose the Resonant Nested Engine (RNE), a cyclic cosmological framework in which theobservable universe behaves as a resonant gravitational cavity with characteristic scale comparable tothe Hubble radius. The model is motivated by the numerical proximity between the Hubble radiusand the Schwarzschild radius associated with the observed cosmic mass–energy content. Cosmicexpansion is interpreted as a low-frequency resonance of coupled scalar degrees of freedom, whilestandard early-universe physics is preserved.The RNE framework introduces a four-field scalar sector whose effective dynamics reduce toΛCDM at redshifts z ≳ 1, ensuring consistency with cosmic microwave background and Big Bangnucleosynthesis constraints. At late times, weak resonant interactions generate a small oscillatorydeviation from a cosmological constant, yielding a redshift-dependent dark-energy equation of statecompatible with current supernovae, baryon acoustic oscillation, and structure-formation bounds.A distinctive prediction of the model is the existence of ultra–low-frequency gravitational-wavecavity modes, with a fundamental frequency f0 ∼ 10−18 Hz, accompanied by horizon-scale echosignatures. These features lie below current pulsar timing array sensitivity but within the projectedstochastic reach of the Laser Interferometer Space Antenna (LISA), providing a direct observationaltest of the RNE scenario.