Fossil Gravity as an Alternative to Dark Matter: A Temporal Extension of General Relativity

This paper proposes a modification of Einstein’s field equation in which the energymomentum tensor is replaced by a weighted integral over past mass distributions. The physical motivation is the finite propagation speed of gravity: at cosmological distances, time offsets of billions of years arise, such that spacetime curvature produced by long-vanished mass structures remains observationally present today. This temporal non-locality — distinct in kind from the spatial non-locality of existing modified gravity theories — offers a unified explanation for three unresolved anomalies: gravitational lensing without sufficient visible mass, flat galactic rotation curves, and the Hubble tension. The model reduces exactly to classical General Relativity in the appropriate limit. Three falsifiable predictions are derived, testable with existing and planned observational programs including the Euclid satellite.