Metric Modulation and Observable Coherence: Deriving an ε-Bound from Fast Radio Burst Phase Statistics within the Sympathetic Harmonic Resonance Framework

This paper derives an observational constraint on a proposed cosmological metric modulation mechanism by analysing the survival of phase coherence in fast radio burst (FRB) signals over gigaparsec propagation distances. A deterministic global modulation of electromagnetic coherence bandwidth with amplitude ε and period T_T produces a cumulative propagation phase shift. Integrating the perturbation along the photon path yields a transfer function linking the modulation amplitude to observable phase variance. The resulting sensitivity kernel is a sinc function, |F| = |sin(π t_prop / T_T)| / (π t_prop / T_T), which defines the regime in which long-baseline propagation experiments are sensitive to the modulation. Applying the coherence survival condition (Δφ_rms < 1 rad) to FRB observations at ~1 GHz over distances of 1–3 Gpc produces an upper bound on the coupling parameter: ε < λ / (L · |F|). For cosmologically plausible modulation periods (T_T ≳ Myr–Gyr), FRB phase coherence constrains the coupling parameter to ε ≲ 10^-24–10^-26, excluding previously viable parameter space by more than twenty orders of magnitude. The modulation route remains viable only if the modulation period is substantially larger than the Hubble time. The analysis identifies observational discriminants separating metric-modulation decoherence from plasma dispersion and scattering, including a ν^-1/5 frequency scaling, a redshift-dependent sinc envelope in coherence statistics, and cross-sightline correlation signatures. These results provide a propagation-physics constraint linking cosmological-scale metric modulation models to existing radio transient observations and establish a framework for further tests using next-generation FRB surveys. Keywords coherence propagationmetric modulationfast radio burstsphase coherencecosmological propagationsinc transfer functionelectromagnetic coherencecoupling parameter epsilonradio transient astrophysicscosmological topologypropagation constraintscoherence bandwidth