Atomic clock constraints on locally coupled scalar dark energy

We show that atomic clock measurements constrain the locally accessible scalar clock combination Δ kₑff√1+w₀ Δ k eff 1 + w 0 for scalar dark energy models coupled to Standard Model sectors. Under the benchmark assumption of weak environmental suppression and an effective scalar clock sensitivity Δ kₑff~ 10⁻⁵ Δ k eff ∼ 10 - 5 , the inferred constraint corresponds to 1+w₀~ 10⁻⁴-10⁻⁵ 1 + w 0 ∼ 10 - 4 - 10 - 5 with a Monte Carlo median 1+w₀ 9.4× 10⁻⁵ 1 + w 0 ≃ 9.4 × 10 - 5 . More conservatively, the result should be interpreted as an exclusion surface in the joint parameter space of scalar coupling, environmental matching, and dark energy dynamics. In this form, atomic clocks and Solar System tests provide a powerful local consistency test for scalar-tensor dark energy, forcing near Λ Λ behavior whenever the same scalar remains locally active and appreciably coupled.