Noether Symmetry in Teleparallel Yang–Mills Cosmology

In this paper, we consider a vector dark energy model based on non-Abelian Yang–Mills theory in the framework of teleparallel gravity. In this framework, instead of the curvature of spacetime determining the gravitational dynamics, the torsion scalar [Formula: see text] is used, and the total action consists of interactions with the scalar field [Formula: see text] that determines the sizes of the three SU(2) vector fields [Formula: see text] that make up the “cosmic triad”. The choice of three vectors of equal size in the three perpendicular directions ensures that anisotropy does not appear in the FLRW field. The model is described by two arbitrary coupling functions [Formula: see text] and [Formula: see text] between the gravitational part and the Yang–Mills part, and a potential [Formula: see text]. By writing a point-like Lagrangian for the cosmic scale variables [Formula: see text] and the effective variable [Formula: see text], the field equations and modified Friedmann equations are derived, and the energy density and effective pressure of this vector fluid are obtained as functions of [Formula: see text] and their derivatives. To avoid ghost-like instability, the effective coupling [Formula: see text] must always be positive. Also, to have [Formula: see text], it is necessary that the Friedmann equation maintain the appropriate sign throughout cosmic evolution. We use the Noether symmetry method to obtain exact solutions, thereby determining the exact forms of the potential and coupling functions, as well as the exact time-dependent scale factor. Our main findings show that, when analyzing the exact solution for recent times, the model reproduces late-time cosmic acceleration. Furthermore, the model is compatible with observations. Specifically, we analyze the five-year sample of Dark Energy Survey Type Ia supernovae (DES-SN5YR) with 1635 supernovae, baryon acoustic oscillation (BAO) measurements from eBOSS DR16, and CMB distance quantities from the 2018 Planck survey. We perform joint fitting using a total likelihood function sampled via Markov chain Monte Carlo (MCMC) algorithms in the Cobaya framework. Our results show that the teleparallel Yang–Mills model with Noether symmetry reproduces the universe’s expansion history, including late-time acceleration, and is consistent with observational data without requiring a purely cosmological constant.