Dark Matter as a Geometric Tension of the Vacuum: A Reformulation of Einstein's Equation

We propose a reformulation of Einstein’s equation without a cosmological constant, introducing a corrective tensor term Fµν representing an internal tension of the vacuum, originating from a diffuse ensemble of micro-cracks in the space-time fabric. This approach models dark matter as a diffuse geometric deformation of the space-time continuum, analogous to topological defects in crystalline media. We demonstrate that this alternative geometric field can reproduce the gravitational effects traditionally attributed to dark matter, without resorting to exotic particles undetected to date. A numerical simulation in a modified FLRW framework highlights compatibility with primordial nucleosynthesis as well as with observed cosmic structure formation. Finally, we offer a critical synthesis of the classic cosmological problems and discuss the perspectives opened by this geometric hypothesis.