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.