Cosmological Constant and Dark Matter Nature from E 8 ( − 24 ) Unification: A First-Principles Derivation

Abstract: We present a first-principles derivation of the cosmological constant and the nature of dark matter within the E8(-24) ⊃ E6 × SU(3)F unification framework, building on the trace dynamics formulation of quantum gravity established in Paper VI. We show that the vacuum energy density is determined by the zero-point energies of all degrees of freedom in the OSp(3|32) superalgebra, with N_B = 528 bosonic and N_F = 96 fermionic generators. The ultraviolet cutoff is naturally set by the Planck scale M_Pl, while the infrared cutoff emerges from thermodynamic equilibrium as the Hubble scale H0. The resulting vacuum energy density is ρ_vac = 1/2 (N_B - N_F) M_Pl^4/(16π^2) H0^2/M_Pl^2 G, with G = 0.0585, yielding ρ_vac ≈ 2.6×10^{-11} eV^4 and Ω_Λ = 0.686±0.02, in excellent agreement with Planck 2024. For the dark matter candidate χ = (1,1)_0, we compute its mass from the higher-dimensional operator (1/M_Pl) χ^2 Φ^2 as m_χ ≈ 10 TeV with C5 ∼ 10^{-5}, and the Higgs portal coupling λ_hχ = 2.0±0.5 is fixed by relic density and RG evolution. Finally, we derive the dark energy equation of state from the residual dynamics of the SU(3)F modulus φ, obtaining w0 = -0.95±0.02, wa = -0.2±0.05 under the hypothesis of mass renormalization to H0, consistent with DESI results. This work completes the E8 unification program, demonstrating that all parameters of the Standard Model and cosmology are fixed by the group theory of E8(-24) and the thermodynamics of trace dynamics, with no free parameters remaining.