What question did this study set out to answer?

The research aims to establish a framework for understanding galactic dynamics through spacetime memory and emergent effects.

March 31, 2026Open Access

Spacetime Memory and Emergent Galactic Dynamics(SM&EGD): A Field-Theoretic Origin of the Observed Acceleration Law

Key Points

The research aims to establish a framework for understanding galactic dynamics through spacetime memory and emergent effects.
Introduced a scalar memory field that accumulates curvature history with non-minimal coupling.
Analyzed the universal acceleration relation using the SPARC galaxy sample.
Derived a late-time dark energy component by adding a small mass term to the potential.
Tested model performance against traditional frameworks like ΛCDM and MOND.
Determined α as (1.20 ± 0.06) × 10−10 m−1/2s, leading to a0 = (0.69 ± 0.07) × 10−10 ms−2.
Showed that the model fits rotation curves across five orders of magnitude in luminosity better than existing models.
Predicted declining outer rotation curves and anomalous weak lensing, which can be tested with future observations.

Abstract

The Spacetime Memory and Emergent Galactic Dynamics (SM&EGD) framework introducesa scalar memory field ϕ that accumulates curvature history through a non-minimalcoupling ξϕR. In the weak-field limit, the field equations yield a universal accelerationrelation a + αa3/2 = aN. Using the SPARC galaxy sample, I obtain α = (1.20 ± 0.06) ×10−10 m−1/2s, corresponding to a0 = (0.69 ± 0.07) × 10−10 ms−2. The model fits rotationcurves across five orders of magnitude in luminosity, outperforming both ΛCDM andMOND. Adding a small mass term to the potential generates a late-time dark energycomponent, and consistency between galactic and cosmological scales forces a0 ∼ cH0with a numerical coefficient matching observations. A non-local memory kernel providesa first-principles foundation, while screening mechanisms ensure Solar System compatibility.The framework resolves the cluster-scale failures of MOND through merger-inducedtidal memory. Distinctive predictions include declining outer rotation curves (vc ∝ r−1/6),anomalous weak lensing, and a scalar gravitational-wave polarisation, all testable with upcomingfacilities.

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