Spectral Gravity–Temperature Cosmology

Title: Spectral Gravity–Temperature Cosmology: A Cyclic Universe from the Renormalization Group Flow on the Spectral Simplex Δ₂ Authors: Petar Iliev Dryanosvski Description: We show that the spectral Renormalization Group (RG) flow on the 3-level simplex Δ₂, defined by a single positive trace-one operator K, generates a complete cyclic cosmology. The spectral weights evolve under entropy-driven RG flow from a hierarchical UV fixed point to a universal maximum-entropy attractor with mean spectral temperature T̄ = log 3. Key results: Scale factor identified as a = 1/T̄, producing natural expansion and contraction phases Friedmann equation derived from spectral action with all terms traced to spectral origins Vacuum equation of state w = -1 and deceleration q_vac = -1 as dynamical consequences Dark energy density Ω_Λ ≈ 0.70, consistent with Planck 2018 CMB temperature calibration: T̄_now ≈ 1.6 × 10⁻¹⁵ in spectral units Primordial power spectrum: n_s ≈ 0.969, r ≈ 5 × 10⁻⁶, α_s ≈ -0.0007 (all matching Planck) Black hole entropy sink enables entropy decrease during cosmic expansion Cyclic cosmology with ~160 Gyr period No cosmological constant, inflaton, or dark energy component introduced All constants derived from the spectral operator K. No free parameters. Numerical verification confirms convergence to log 3 at machine precision. The Friedmann equation, FLRW metric, and CMB power spectrum all emerge from the spectral geometry. Based on the Spectral Dictionary (Zenodo: 10.5281/zenodo.20343026)