Cosmological redshift as a manifestation of nonlinear critical relativistic quantum wave fields

We explore the hypothesis that both Newtonian and relativistic gravitational phenomena may emerge from critical dynamics in nonlinear relativistic wave fields, in analogy with wave–particle duality in quantum systems. Using a general nonlinear self-adjoint wave Hamiltonian, we construct a set of illustrative toy models in which increasing interaction strength drives a transition from extended, oscillatory waves to localized particle-like excitations. In this framework, gravitational and cosmological effects—including redshift—arise as collective, near-critical wave phenomena rather than as properties of a predefined spacetime geometry. The constancy of the speed of light emerges from nonlinear terms in the dispersion relation, and wave localization provides a common origin for inertial and gravitational mass without requiring a separate equivalence principle. These models also exhibit the absence of singularities (e.g., at the Schwarzschild radius or at r = 0 ) and suggest potential connections between local gravitational behavior and large-scale structure. As a proof of concept, we show how critical-wave effects may alleviate the observed tension between Planck CMB inferences and supernova/Cepheid distance measurements without assuming FLRW metrics or Λ CDM dynamics; the same mechanism provides an alternative simple explanation for the BAO peak in the galaxy distribution function. We emphasize that these results are not proposed as a replacement for general relativity or standard cosmology, but as a conceptual demonstration that nonlinear wave dynamics can reproduce qualitative gravitational and cosmological features, motivating further investigation into emergent-gravity scenarios.