Stability-Protected Phantom Bound in Scalar-Field Cosmology

Abstract: Recent cosmological observations, most notably from the DESI Data Release 2 (DR2) \cite{DESIDR2}, suggest a potential redshift evolution of the dark energy equation of state, reviving fundamental questions regarding the physical viability of the phantom regime ($w < -1$). In this Letter, a no-go result is established for a broad class of single-field effective scalar cosmologies where the kinetic response is modulated by the Hubble expansion rate, a structural feature characteristic of infrared-modified and nonlocal gravity theories \cite{DeserWoodard2007, Maggiore2014}. It is proved that imposing ghost freedom, defined by the positivity of the kinetic response function $\mathcal{M} \equiv \partialρ/\partial X > 0$, enforces the phantom divide ($w = -1$) as a \textit{stability-protected boundary} in the cosmological phase space. While the equation of state can approach this limit arbitrarily closely, continuous ghost-free evolution into the phantom regime is shown to be strictly forbidden. The dynamics are found to converge toward a de~Sitter-like attractor where $w \to -1$ emerges as a consequence of dynamical selection and stability rather than the fine-tuning of the scalar potential. These results suggest that the "hints" of evolution observed in DESI DR2 may reflect the underlying stability requirements of the effective field theory, providing a theoretical mechanism that prevents a physical transition into the phantom phase.