Total Coherent Theory (TCT): Vacency Coherence, Emergent Lorentz Symmetry, and Cosmological Predictions including Low-ℓ CMB Modulations

Total Coherent Theory v2 (TCT-v2) presents a theoretical framework in which the vacuum is modeled as a coherent physical state rather than as a passive background. The theory introduces a coherent doublet field, Ψ=(ψ,λ),\Psi = (\psi,\lambda),Ψ=(ψ,λ), endowed with an Algebra of Total Coherence (ACT), and explores how spacetime propagation, effective constants and cosmological evolution may emerge from this coherent-vacuum structure. This version strengthens the cosmological sector of TCT by deriving a dynamical scaling relation between coherent-vacuum perturbations and a preferred low-multipole angular scale in the cosmic microwave background. Perturbing the coherent vacuum as Ψ(x⃗,t)=Ψ0+δΨ(x⃗,t),\Psi(\vec{x},t)=\Psi_0+\delta\Psi(\vec{x},t),Ψ(x,t)=Ψ0+δΨ(x,t), and using a quartic coherent potential, the framework obtains an effective perturbation mass mΨ2=2λΨ02.m_\Psi^2 = 2\lambda\Psi_0^2.mΨ2=2λΨ02. In a FLRW background, the transition between gradient-dominated and mass-dominated coherent perturbations selects a characteristic coherent wavenumber, kΨ=ηΨaeffmΨ,k_\Psi = \eta_\Psi a_{\rm eff} m_\Psi,kΨ=ηΨaeffmΨ, which projects onto the last-scattering sphere as ℓTCT≃kΨχ∗.\ell_{\rm TCT} \simeq k_\Psi \chi_*.ℓTCT≃kΨχ∗. For a coherent scale kΨ∼10−3 Mpc−1k_\Psi \sim 10^{-3}\,{\rm Mpc}^{-1}kΨ∼10−3Mpc−1, the predicted angular scale is ℓTCT∼17,\ell_{\rm TCT} \sim 17,ℓTCT∼17, with a finite modulation width naturally mapping this value into the approximate interval 14≤ℓ≤2014 \leq \ell \leq 2014≤ℓ≤20. The expected observational signature is not a sharp spectral line, but a smooth low-ℓ\ellℓ modulation, with a negative CMB–Large Scale Structure residual amplitude corresponding to a valley-like suppression of correlation efficiency. The paper also discusses the emergence of Lorentz symmetry from a homogeneous coherent vacuum, formal vacuum-dependent effective constants G(Ψ)G(\Psi)G(Ψ), α(Ψ)\alpha(\Psi)α(Ψ), Λeff(Ψ)\Lambda_{\rm eff}(\Psi)Λeff(Ψ), limiting cases recovering GR, ΛCDM, scalar–tensor gravity, quintessence-like behavior and varying-constant frameworks, as well as explicit falsifiability conditions for the predicted low-ℓ\ellℓ modulation. The work is theoretical. It does not claim to prove the observed CMB anomaly, nor does it present a complete first-principles numerical derivation of ℓTCT=17\ell_{\rm TCT}=17ℓTCT=17. Instead, it formulates a testable dynamical scaling prediction linking coherent-vacuum relaxation to a preferred low-ℓ\ellℓ cosmological signature. The observational test is intended to be developed in a separate companion analysis based on CMB–LSS residual spectra, component-separated CMB maps, Gaussian mock realizations and multipole-space statistics.