A Modified Gravitational Wave Equation Model: Coupling of Spacetime Shock Perturbation, Dark Matter Damping and Dark Energy Cosmological Modulation

Standard general relativity treats gravitational waves as pure spacetime geometric fluctuations propagating in ideal vacuum, which cannot fully explain the observed waveform attenuation, high-frequency smoothing, and the origin of the nanohertz gravitational wave background. To resolve the inconsistency between theoretical prediction and actual cosmic observation, this paper proposes a three-component unified coupling model. We verify that real cosmic gravitational waves are comprehensively determined by three physical mechanisms: spacetime shock perturbation generated by compact object mergers, damping and scattering effects of the universal dark matter medium, and continuous spectral modulation caused by dark energy-driven cosmic expansion. We derive a self-consistent modified gravitational wave field equation and dispersion relation that naturally explains wave amplitude decay, frequency redshift, and large-scale low-frequency background formation. The model maintains logical compatibility with general relativity while introducing dark component correction terms, providing a new theoretical framework for studying gravitational wave propagation effects and dark cosmic physical properties.

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