Stability Protected Phantom Bound in Expansion Modulated Cosmology

Recent cosmological observations, including DESI Data Release 2 (DR2) \cite{DESIDR2}, allow for mild redshift evolution of the dark energy equation of state (EoS), motivating renewed interest in the phantom regime ($w<-1$). A no-go result is presented for a class of single field effective scalar cosmologies with Hubble modulated kinetic response, as motivated by infrared modified and nonlocal gravitational frameworks \cite{DeserWoodard2007,Maggiore2014}. Imposing ghost freedom, $\mathcal{M}\equiv \partial\rho_\phi/\partial X>0$, renders the phantom divide ($w_\phi=-1$) an invariant and dynamically stable manifold of the cosmological flow, extending standard kinematical no-go theorems to a dynamical systems framework. Continuous ghost free evolution into the phantom regime is forbidden, although $w_\phi\to -1$ can be approached asymptotically. The late time dynamics generically converge to a de~Sitter like attractor driven by expansion induced kinetic suppression rather than potential fine tuning. These results clarify the role of stability constraints in shaping late time cosmic acceleration in single field effective scalar cosmologies.