All Quiet on the Vector Front: Scalar Growth and Perturbative Control in Horndeski--Weyl-squared Gravity
Abstract
Higher-order curvature corrections to general relativity arise naturally in many fundamental theories and provide phenomenologically interesting low-energy effective field theories. However, higher-derivative terms can introduce ghost modes, which call the validity of such models into question. Here, we thoroughly investigate the classical linear stability of the most general second-order scalar-tensor theory, namely the Horndeski theory of gravity, augmented by a Weyl-squared term in the action. We consider shift-symmetric de Sitter and power-law FLRW backgrounds and study the evolution of linear perturbations. Vector perturbations are free of gradient and tachyonic instabilities for a positive Weyl-induced mass squared. Tensor perturbations necessarily contain a ghost; their superhorizon branches are bounded, while a frozen-background calculation identifies a separate finite-momentum stability condition. The scalar sector instead contains a growing long-wavelength branch for all expanding backgrounds we consider, which is inherited by at least one of the gauge-invariant Bardeen potentials. We show that this growth enters the Bardeen potentials through an inverse-gradient factor a2/k2: the dynamical scalar fields remain bounded on the inflationary backgrounds, the direct contribution of the growing shear to the clock-matched tidal field cancels, and the electric part of the Weyl tensor decays. We discuss the implications of our results for perturbative control and for the phenomenological viability of theories including quadratic curvature corrections.
Related
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BibTeX
@misc{felice2026quiet,
title = {{All Quiet on the Vector Front: Scalar Growth and Perturbative Control in Horndeski--Weyl-squared Gravity}},
author = {Antonio De Felice and Guillem Domènech and Jan Tränkle},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20156},
eprint = {2610.20156},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20156},
}
RIS
TY - UNPB
TI - All Quiet on the Vector Front: Scalar Growth and Perturbative Control in Horndeski--Weyl-squared Gravity
AU - Antonio De Felice
AU - Guillem Domènech
AU - Jan Tränkle
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20156
UR - https://arxiv.org/abs/2610.20156
AB - Higher-order curvature corrections to general relativity arise naturally in many fundamental theories and provide phenomenologically interesting low-energy effective field theories. However, higher-derivative terms can introduce ghost modes, which call the validity of such models into question. Here, we thoroughly investigate the classical linear stability of the most general second-order scalar-tensor theory, namely the Horndeski theory of gravity, augmented by a Weyl-squared term in the action. We consider shift-symmetric de Sitter and power-law FLRW backgrounds and study the evolution of linear perturbations. Vector perturbations are free of gradient and tachyonic instabilities for a positive Weyl-induced mass squared. Tensor perturbations necessarily contain a ghost; their superhorizon branches are bounded, while a frozen-background calculation identifies a separate finite-momentum stability condition. The scalar sector instead contains a growing long-wavelength branch for all expanding backgrounds we consider, which is inherited by at least one of the gauge-invariant Bardeen potentials. We show that this growth enters the Bardeen potentials through an inverse-gradient factor a^2/k^2: the dynamical scalar fields remain bounded on the inflationary backgrounds, the direct contribution of the growing shear to the clock-matched tidal field cancels, and the electric part of the Weyl tensor decays. We discuss the implications of our results for perturbative control and for the phenomenological viability of theories including quadratic curvature corrections.
ER -