Cumulative Elastic Stress in Spacetime: An Explanation of Dark Matter Phenomena without Graviton Mass

I propose a modified-gravity framework where dark matter phenomena arise from cumulative elastic stress in spacetime, encoded in a scalar memory field ϕ with a linear potential V (ϕ) = λϕ and non-minimal coupling ξϕR. A rigorous perturbative analysis demonstrates the graviton remains strictly massless, ensuring exact consistency with the gravitational-wave constraint |cgw/c − 1| < 10−15 from GW170817. In the weakfield, quasi-static regime, the field equations reduce to a modified acceleration relation, a + αa3/2 = aN, where aN is the Newtonian acceleration. This relation is derived asymptotically from the coupled field equations, and introduces a characteristic acceleration scale a0 = α−2. Fitting this single-parameter relation to 175 galaxies from the SPARC database—marginalizing over stellar mass-to-light ratios with Gaussian priors—yields a universal parameter α = (1.20 ± 0.06) × 10−10 m−1/2s (corresponding to a0 ≈ 0.69 × 10−10 ms−2) with a mean reduced chi-square ⟨χ2ν⟩ ≈ 1.12. The model successfully reproduces observed galactic rotation profiles across five orders of magnitude in luminosity and predicts an asymptotic velocity scaling vc ∝ r−1/6 from the dominant dynamical balance in the field equations, providing a testable discriminant from MOND. At cluster scales, merger-induced tidal stress naturally generates the enhanced mass discrepancy observed in systems such as the Bullet Cluster and CLASH data. The same memory field yields a late-time dark-energy component with equation of state w(z) ≈ −1+O(H2 0/H2), unifying galactic and cosmic acceleration scales.