A late time accelerated FRW model with scalar and vector fields via Noether symmetry

TL;DR

This paper uses Noether symmetry to analyze a cosmological model with scalar and vector fields, deriving exact solutions that describe an accelerated universe driven by vector fields early on and scalar fields later.

Contribution

It explicitly determines the form of the scalar-vector coupling and potential functions that admit Noether symmetry, leading to exact cosmological solutions.

Findings

The model predicts accelerated expansion driven by vector fields in early times.

Scalar fields dominate the late-time accelerated expansion.

Exact solutions for the scale factor, scalar, and vector fields are obtained.

Abstract

We study the evolution of a three-dimensional minisuperspace cosmological model by the Noether symmetry approach. The phase space variables turn out to correspond to the scale factor of a flat Friedmann-Robertson-Walker (FRW) model, a scalar field with potential function $V(\phi)$ with which the gravity part of the action is minimally coupled and a vector field of its kinetic energy is coupled with the scalar field by a coupling function $f(\phi)$. Then, the Noether symmetry of such a cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generator of the desired symmetry. We explicitly calculate the form of the coupling function between the scalar and the vector fields and also the scalar field potential function for which such symmetry exists. Finally, by means of the corresponding Noether current, we integrate the equations of motion and obtain exact solutions for the scale factor, scalar and vector fields. It is shown that the resulting cosmology is an accelerated expansion universe for which its expansion is due to the presence of the vector field in the early times, while the scalar field is responsible of its late time expansion.