Geometric Cold Dark Matter from Inflation-Generated Local Spacetime Fragments in Scalar-Gauss-Bonnet Gravity

We propose a purely geometric dark matter candidate: Local Spacetime Fragments (LSFs)—stable topological solitons formed during preheating in scalar–Gauss–Bonnet gravity. The action includes a coupling f(\phi)\mathcal{G}, where \mathcal{G} is the Gauss–Bonnet invariant. During preheating, parametric resonance amplifies \mathcal{G} above a critical threshold \mathcal{G}_c \sim M_{\rm Pl}^4, triggering a tachyonic instability that fragments spacetime into LSFs carrying a conserved topological charge \pi_3(S^3). The auxiliary field \phi decays after fragmentation, leaving LSFs as purely gravitational objects. The LSF mass function follows a log-normal distribution with mean m_0 \approx 10^3 M_{\rm Pl} and width \sigma \approx 0.5, yielding the observed dark matter abundance and a naturally peaked mass spectrum consistent with cold dark matter phenomenology. The model provides a unified geometric origin for dark matter, linking it directly to the quantum-gravitational structure of spacetime without invoking new fundamental particles.