A Unified Primitive Tensor Approach with EFT-Consistent Deviation: Gravitational Wave Signatures

This work presents a mathematically explicit minimal formulation inspired by the Unified Primitive Theory (UPT) framework. UPT proposes that conventional physical observables may be interpreted as projections of a single primitive tensorial structure. To render this conceptual approach operational and empirically testable, we introduce a controlled effective field theory (EFT) deviation confined to the gravitational tensor sector. The modification preserves covariance, avoids higher-derivative instabilities, and recovers general relativity (GR) exactly in the limit of vanishing deviation. The resulting dynamics predict a modified dispersion relation for gravitational waves, leading to frequency-dependent propagation effects. We derive the tensor-mode equations of motion via a variational principle, analyse linearised solutions in Minkowski and Friedmann–Robertson–Walker (FRW) backgrounds, and obtain explicit expressions for group velocity, phase corrections, and arrival-time delays. Observational implications are discussed in the context of modern gravitational wave constraints. This manuscript represents a minimal operationalisation of a unified primitive tensor concept within an EFT-consistent setting.