Noether Symmetries of SU(2) Yang–Mills Dark Energy in Nonmetricity Gravity

We investigate an isotropic SU(2) Yang–Mills cosmic triad in symmetric teleparallel, or nonmetricity, gravity. The model contains a non-minimal coupling [Formula: see text], a field-dependent Yang–Mills kinetic coupling [Formula: see text], and a self-interaction potential [Formula: see text], where [Formula: see text] is the invariant of the homogeneous triad. After the minisuperspace reduction, the background dynamics is written in terms of the effective functions, and then we derive the effective energy density, pressure, and equation-of-state parameter, and identify the conditions under which the system approaches a vacuum-like accelerated regime. The Noether symmetry method is then applied to the point-like Lagrangian. For a monomial effective potential, the determining equations lead to three algebraic branches. The first branch is degenerate and removes the non-minimal coupling, while the regular sectors of Branch II and Branch III admit cyclic variables and exact cosmological solutions. The effective-fluid adiabatic response is evaluated for the exact solutions and is distinguished from the propagation properties of the underlying perturbations. At the principal level, the metric and Yang–Mills tensor modes both propagate luminally at high frequency, while the necessary tensor no-ghost and high-wavenumber gradient conditions are [Formula: see text] and [Formula: see text]. These conditions identify tensor-safe candidate regions for Branch II and Branch III, whereas the scalar and vector sectors require a separate covariant quadratic analysis. Numerical examples illustrate accelerated expansion, with Branch II realizing a dynamical-invariant quasi-de Sitter behavior and Branch III approaching a constant-invariant de Sitter-like regime.