What question did this study set out to answer?

The aim is to derive the memory kernel from a variational principle within the History-Dependent Gravity framework.

July 7, 2026Open Access

Dark Matter as Temporal Nonlocality: Variational Derivation of the Memory Kernel (Paper XV in the History-Dependent Gravity Series)

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Demonstrates how dark matter behavior arises from a nonlocal gravitational model, suggesting profound implications for gravity theory.

The aim is to derive the memory kernel from a variational principle within the History-Dependent Gravity framework.
Developed a causal, nonlocal modification of gravity based on a derived memory kernel.
Introduced a gravitational action formulation with specific constraints on causality, dimensional consistency, and absence of ghosts.
Evaluated the model's compatibility with observational phenomena such as galactic rotation curves and gravitational wave constraints.
The temporal memory kernel was derived as K(t-t') ~ 1/(t-t') · exp(-(t-t')/τ), satisfying action-level consistency.
Achieved quantitative fits to galactic rotation curves in M33, revealing a ~25% tension with the standard acceleration scale.
Demonstrated consistency with early-universe cosmology and gravitational wave propagation at high frequencies.

Alik Gimranov (2026) studied this question.

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