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Stability-Protected Phantom Bound in Scalar-Field Cosmology

Prasanta Sahoo

TL;DR

The paper analyzes whether phantom crossing ($w<-1$) can occur in single-field scalar cosmologies with a kinetic term suppressed by the cosmic expansion. By imposing ghost freedom through $\mathcal{M}=\partial\rho_\phi/\partial X>0$ in a flat FLRW background with a Hubble-modulated kinetic term, it proves that the phantom divide $w=-1$ is a stability-protected boundary and continuous crossing is forbidden. The dynamics generically flow toward a de Sitter-like attractor with $w\to -1$ due to expansion-induced kinetic suppression, rather than fine-tuning of the potential. Observationally, mild redshift evolution of $w(z)$ compatible with DESI DR2 can be viewed as a manifestation of underlying stability, with $H(z)$ remaining close to $\Lambda$CDM; the results hold within the single-field effective description and invite extensions to multi-field or beyond-Horndeski scenarios for phantom crossing.

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 $\mathcal{M} \equiv \partialĪ/\partial X > 0$, 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.

Stability-Protected Phantom Bound in Scalar-Field Cosmology

TL;DR

The paper analyzes whether phantom crossing () can occur in single-field scalar cosmologies with a kinetic term suppressed by the cosmic expansion. By imposing ghost freedom through in a flat FLRW background with a Hubble-modulated kinetic term, it proves that the phantom divide is a stability-protected boundary and continuous crossing is forbidden. The dynamics generically flow toward a de Sitter-like attractor with due to expansion-induced kinetic suppression, rather than fine-tuning of the potential. Observationally, mild redshift evolution of compatible with DESI DR2 can be viewed as a manifestation of underlying stability, with remaining close to CDM; the results hold within the single-field effective description and invite extensions to multi-field or beyond-Horndeski scenarios for phantom crossing.

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 (). 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 , enforces the phantom divide () 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 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.
Paper Structure (8 sections, 2 theorems, 21 equations, 1 figure)

This paper contains 8 sections, 2 theorems, 21 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Effective Framework and Stability Bound
  3. Asymptotic Dynamics
  4. Covariant Origin from Nonlocal Gravity
  5. Universal Stability Bound on Phantom Crossing
  6. Observational Illustration
  7. Linear Perturbations and Stability
  8. Conclusion

Key Result

Theorem 1

Consider a spatially flat FLRW cosmology governed by Einstein gravity and containing a single homogeneous scalar degree of freedom with effective pressure $P_\phi=P(X,H,\phi)$. Assume: (i) background energy conservation; (ii) ghost-free kinetic response, $\partial P_\phi/\partial X \ge 0$ and $\part

Figures (1)

  • Figure 1: Redshift evolution of the equation of state $w_{\phi}(z)$ (top) and the ratio $H(z)/H_{\Lambda{\rm CDM}}(z)$ (bottom). Dashed lines indicate $\Lambda$CDM reference values. The equation of state approaches $w=-1$ at low redshift without crossing, while the expansion history remains close to $\Lambda$CDM.

Theorems & Definitions (4)

  • Theorem 1: Stability-protected phantom bound
  • proof
  • Theorem 2: Universal stability bound underlying Theorem \ref{['thm:phantom_nogo_PRL']}
  • proof