KREG-IV: Constraints on Minimal Luminal EFT Models from Stability and Growth-Lensing Consistency

We investigate whether minimal luminal Effective Field Theory of Dark Energy (EFT-of-DE) models can produce observable deviations from ΛCDM while remaining stable and consistent with current cosmological constraints. Using a numerical parameter scan over a minimal EFT parametrization, we apply theoretical stability conditions (absence of ghost and gradient instabilities) together with observational consistency requirements derived from large-scale structure probes, including growth and lensing observables (μ, Σ, E_G). We find that although stable regions formally exist, the imposition of realistic growth–lensing consistency conditions leads to a collapse of the viable parameter space. This indicates a strong tension between stability, observational consistency, and detectability in minimal scalar–tensor modifications of gravity. Our results suggest that any observable deviation from General Relativity within the EFT-of-DE framework likely requires non-minimal structure, such as scale-dependent effects or extended couplings beyond the minimal parametrization.