Scalar-Cost Dark Energy (SCDE) II: RG Running, Decoupling, and EFT Expansion

This paper provides a first-principles derivation of Scalar-Cost Dark Energy (SCDE) within the effective field theory of a single-clock cosmology. SCDE I (Brown 2025) introduced the phenomenological framework and showed that a scalar field with time-dependent kinetic normalization K(t) can preserve a ΛCDM background while generating measurable kineticity-only signatures in large-scale structure. Here, the theoretical foundation of the model is established. Under four assumptions—locality and diffeomorphism invariance, an unmodified Einstein–Hilbert sector with constant reduced Planck mass, a two-derivative truncation, and a single FRW clock—the scalar sector is shown to be uniquely equivalent, after restoring time diffeomorphisms, to a minimally coupled field with covariant Lagrangian P(X, φ, t) = K(t) X − V(φ),with X ≡ −½ gμν ∂_μ φ ∂_ν φ. General Relativity and tensor propagation remain standard (cₜ = 1), consistent with GW170817 constraints (Abbott et al. 2017; Creminelli & Vernizzi 2017; Baker et al. 2017; Ezquiaga & Zumalacárregui 2017). Two established QFT mechanisms naturally generate a smooth, adiabatic K(t) on FRW backgrounds: (i) renormalization-group improved wavefunction normalization with a background sliding scale, and (ii) decoupling of a heavy curvature-sensitive mediator. Stability conditions, validity bounds, and implementation details are summarized. Together with SCDE I, this work completes a conservative, fully motivated, and observationally testable extension of the ΛCDM scalar sector derived directly from established physics.