Spectral Hierarchy of the Cosmological Constant, Mukhanov–Sasaki Derivation,Scale Separation,and Primordial Observational Signatures

This is Paper 2 of a three-part program on the spectral selection of the cosmological constant. Paper 1 (https: //doi. org/10. 5281/zenodo. 18736246) established that the cosmological constant Λ emerges as the ground-state eigenvalue of a Wheeler–DeWitt effective potential derived from quantum and instanton contributions. That paper identified two open problems: the semi-quantitative nature of the predicted primordial power spectrum modification and the absence of a derivation connecting the quantum structure to the Standard Model electromagnetic sector. This paper (Paper 2) addresses the first of these problems. Starting from the full cosmological action with Λ treated as a dynamical quantum degree of freedom, the spectral structure Λₙ = Λ₀ + nΔΛ is propagated through the Friedmann equations into the Mukhanov–Sasaki equation for scalar curvature perturbations. The key results are: A rigorous derivation of how the Wheeler–DeWitt ground-state zero-point fluctuations act as a periodic perturbation to the inflationary dynamics. The analytical demonstration that this perturbation generates a log-periodic modulation of the primordial curvature power spectrum, with an amplitude A ∼ 10⁻³ and a frequency ω_Λ/H ∼ 10–100, both derivable from the parameters of the effective potential introduced in Paper 1. The identification of a critical scale separation between the late-universe vacuum energy Λ₀ and the inflationary Hubble scale Hᵢnf, resolving a potential confusion in preliminary treatments. A spectral hierarchy showing that each Wheeler–DeWitt eigenstate produces a distinct primordial spectrum, linking the quantum structure of Λ to a cosmological hierarchy of possible universes. Observational predictions that distinguish this mechanism from other models such as axion monodromy inflation: suppressed non-Gaussianity (fNL ∼ 10⁻⁶), an oscillatory scale-dependent correction to the spectral index nₛ of order 10⁻², and consistency with current bounds from Planck, ACT, and SPT. The predicted amplitude is within reach of next-generation experiments like CMB-S4. An explicit statement of the most critical open problem: the conversion of the rescaled Wheeler–DeWitt oscillation frequency to physical units, which would sharpen the amplitude prediction from a self-consistency argument to a first-principles result. Paper 3 (in preparation) will embed this spectral selection in a cyclic cosmological framework, explaining why the universe is in the ground state n = 0 and fixing the oscillation phase φ₀ through entropy transfer between cycles.