No-Go Theorem for Phantom Crossing in Scalar-Tensor Gravity with Non-Minimal Derivative Coupling and Soft Scale-Invariance Breaking
Abstract
Recent baryon acoustic oscillation measurements from the Dark Energy Spectroscopic Instrument (DESI 2024) reveal a preference for dynamical dark energy with an equation of state parameter crossing the phantom divide (w < −1) at low redshifts. We investigate whether this phantom crossing can be realized within scale-invariant scalar-tensor theories featuring non-minimal derivative coupling (NMDC) between the scalar field and the Einstein tensor. Employing the effective field theory of dark energy formalism, we systematically derive the ghost-free and gradient stability conditions, and examine their compatibility with the swampland conjectures from quantum gravity. We establish three rigorous no-go theorems demonstrating that: (i)~phantom crossing necessitates ξeff < 0, directly violating the no-ghost stability requirement ξeff > 0; (ii)~the swampland de Sitter and distance conjectures independently obstruct phantom crossing; and (iii)~these theoretical obstructions are mutually reinforcing. Our results show that scale-invariant NMDC models cannot account for the DESI preference for w < −1, providing robust theoretical guidance for dark energy model building beyond this class.
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BibTeX
@misc{baghbani2026nogo,
title = {{No-Go Theorem for Phantom Crossing in Scalar-Tensor Gravity with Non-Minimal Derivative Coupling and Soft Scale-Invariance Breaking}},
author = {Reza Baghbani},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14354},
eprint = {2610.14354},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14354},
}
RIS
TY - UNPB
TI - No-Go Theorem for Phantom Crossing in Scalar-Tensor Gravity with Non-Minimal Derivative Coupling and Soft Scale-Invariance Breaking
AU - Reza Baghbani
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.14354
UR - https://arxiv.org/abs/2610.14354
AB - Recent baryon acoustic oscillation measurements from the Dark Energy Spectroscopic Instrument (DESI 2024) reveal a preference for dynamical dark energy with an equation of state parameter crossing the phantom divide (w < −1) at low redshifts. We investigate whether this phantom crossing can be realized within scale-invariant scalar-tensor theories featuring non-minimal derivative coupling (NMDC) between the scalar field and the Einstein tensor. Employing the effective field theory of dark energy formalism, we systematically derive the ghost-free and gradient stability conditions, and examine their compatibility with the swampland conjectures from quantum gravity. We establish three rigorous no-go theorems demonstrating that: (i)~phantom crossing necessitates ξ_eff < 0, directly violating the no-ghost stability requirement ξ_eff > 0; (ii)~the swampland de Sitter and distance conjectures independently obstruct phantom crossing; and (iii)~these theoretical obstructions are mutually reinforcing. Our results show that scale-invariant NMDC models cannot account for the DESI preference for w < −1, providing robust theoretical guidance for dark energy model building beyond this class.
ER -