A Gauss–Bonnet Mass-Drift Degeneracy Criterion for Apparent Phantom Crossing

Apparent phantom crossing in late-time cosmology does not necessarily require a fundamental phantom fluid. It may also emerge from an incorrect separation of dark-matter and dark-energy components when the reconstructed expansion history is interpreted under the standard assumption of conserved cold dark matter. In this work, we formulate a model-independent degeneracy criterion for apparent phantom behavior in the presence of a geometrically induced drift of the effective dark-matter mass. We consider a dark-matter density of the form $\rho_\chi(a)=\rho_{\chi 0}a^{-3}\mu(a)$, where $\mu(a)=m_{\rm eff}(a)/m_{\rm eff}(1)$, and allow the mass-drift function to be sourced by a Gauss–Bonnet response, $m_{\rm eff}=m_{\rm eff}(\mathcal{G})$, with $\mathcal{G}=24H^2(H^2+\dot H)$. If the same background expansion is reconstructed by assuming $\rho_\chi\propto a^{-3}$, the inferred dark-energy density is shifted by the mismatch between the true and assumed dark-matter dilution laws. We derive the resulting apparent equation of state and show that a positive mass-drift index, $\Xi(a)=d\ln\mu/d\ln a$, can drive $w_{\rm app}<-1$ even when the underlying dark-energy component remains non-phantom. The proposed criterion provides a compact diagnostic for distinguishing genuine phantom evolution from geometrically induced dark-sector misidentification. This framework is relevant for Gauss–Bonnet cosmologies, effective dark-energy reconstruction, and regular phantom-like scenarios without introducing a fundamental phantom degree of freedom.