Invariant Electric Charge and the GeometricOrigin ofMass A Two-Metric Projection Theory of Gravity andCosmology

This paper presents a geometric theory based on a newfundamental principle: the invariance of electric charge in allreference frames and gravitational potentials. The theoryintroduces a two-metric structure in which each elementaryparticle possesses an internal metric with its own invariantinteraction velocity, in addition to an external spacetime metriccharacterized by the speed of light. Electric charge is defined asa geometric invariant of the internal metric, while mass arisesas a non-fundamental quantity resulting from the projectionbetween internal and external causal structures.Gravity is described by standard Einstein equations, butwith a modified source defined by the projection of theenergy-momentum tensors of internal particles onto theexternal metric. This approach naturally explains the origin ofmass, the universality of electric charge, the phenomenology ofdark matter, the deviations between dynamical and lensingmass, and the characteristic features of the anisotropies of thecosmic microwave background, without modifying GeneralRelativity or introducing additional fields.