Analytical Solutions for Vector Dark Energy Model via Noether Symmetry

In this work, we study a vector dark energy (vDE) model within the framework of a flat Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. By using the Noether symmetry approach, we obtain analytical cosmological solutions. The vDE model includes a vector field [Formula: see text] coupled to gravity through an arbitrary coupling function [Formula: see text] and a potential function [Formula: see text], which are determined by imposing Noether symmetry conditions. These conditions yield specific forms for the coupling and potential functions, enabling the simplification of the dynamical system. By introducing new variables [Formula: see text] and [Formula: see text], we solve the field equations and obtain exact solutions for the scale factor [Formula: see text] and the vector field parameter [Formula: see text]. In this paper, we adopt the potential function in the form [Formula: see text] and derive solutions for general [Formula: see text]. We specifically examine the cases [Formula: see text] and [Formula: see text], which produce physically viable results consistent with late-time cosmic acceleration. Graphical representations of the scale factor, vector field parameter, and equation of state demonstrate the transition from a matter-dominated era to an accelerated expansion phase, with the equation of state approaching [Formula: see text], resembling a cosmological constant. This paper suggests that the vDE model is a proper candidate for dark energy.