The Cosmological Glass of the Euler Universe: Dark energy and dark matter as the elastic and viscoelastic response of the de Sitter horizon

Euler Cosmos series [S16]. This working paper completes the entropic-gravity framework of [S15] by adding one axiom — that the universe began at low coarse-grained entropy and climbs monotonically toward the de Sitter horizon maximum — and reading the dark sector as the mechanical response of a cosmological "glass": a medium held out of its own equilibrium by the arrow of time. The instantaneous (elastic) response of the medium is identified with dark energy and its slow (viscoelastic, relaxation) response with dark matter, unified as the two frequency limits of one horizon entropy. The elastic modulus is derived as K = s_V k_B T_dS = ρ_Λ c² (the de Sitter density); the medium's longitudinal wave speed comes out equal to c, recovering the dark-energy sound speed the series had previously assumed; and the galactic acceleration scale is a₀ = c / τ_rel, the speed of light over the medium's relaxation time. The framework converts the one open dynamical question of [S15] into a transport-coefficient question, brackets the coefficient of a₀ to order unity from horizon dynamics and the Kovtun–Son–Starinets viscosity bound, and locates its residual as the mass of a de Sitter matter operator in the double-scaled SYK dual. Claims are graded throughout as forced, fits, or conjecture; the low-entropy initial condition is carried as an explicit underived input. The single free coefficient is left to be measured, four coupled ways, by DESI DR3, Euclid/Roman rotation curves, and Gaia wide binaries. Claude (Anthropic)