Existence of dual matter in the theory of dual relativity

The theory of dual relativity (TDR) posits two kinds of matter—ordinary and dual—whose dynamics are governed by two metrics related through $$\tilde{g}_{\mu\nu} = \gamma_{\mu\lambda} g^{\lambda\kappa} \gamma_{\kappa\nu}$$, with $\gamma$ a background flat metric. In the Newtonian limit derived in the paper, ordinary matter particles have positive gravitational masses equal to their inertial masses, while dual matter particles have negative gravitational masses (with positive inertial masses), leading to repulsive (antigravitational) interactions between ordinary and dual matter.

The cosmological analysis summarized in the paper indicates that certain desirable features—such as solutions corresponding to a stable Universe with equilibrium metric matching the background—require the presence of both ordinary and dual matter. Despite these theoretical motivations, the authors explicitly state that whether dual matter exists remains an open question.