Analytical solutions for vector dark energy model via Noether symmetry

Akbarieh A. R., Sorkhab F. M., KÜÇÜKAKÇA Y., Bolouri M. A.

International Journal of Geometric Methods in Modern Physics, 2026 (SCI-Expanded, Scopus)

Özet

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 Aμ coupled to gravity through an arbitrary coupling function f(ξ) and a potential function V (ξ), 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 u and z, we solve the field equations and obtain exact solutions for the scale factor a(t) and the vector field parameter ξ(t) = AμAμ. In this paper, we adopt the potential function in the form V (ξ) = V0ξn and derive solutions for general n. We specifically examine the cases n = 1 and n = 2, 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 − 1, resembling a cosmological constant. This paper suggests that the vDE model is a proper candidate for dark energy.