Noether Symmetry Approach in "Cosmic Triad" Vector Field Scenario

TL;DR

This paper employs the Noether symmetry approach to identify suitable potentials in the cosmic triad vector field scenario, aiming to explain cosmic acceleration and dark energy behavior.

Contribution

It introduces a systematic method to derive potentials for vector fields in cosmology using Noether symmetries, including solutions for quintessence, phantom, and quintom models.

Findings

Constant potential solutions for quintessence and phantom models.

A power-law potential solution with rapid decay in the quintessence model.

A specific constraint on potentials in the quintom model involving Noether symmetry.

Abstract

To realize the accelerations in the early and late periods of our universe, we need to specify potentials for the dominant fields. In this paper, by using the Noether symmetry approach, we try to find suitable potentials in the "cosmic triad" vector field scenario. Because the equation of state parameter of dark energy has been constrained in the range of $-1.21\leq \omega\leq -0.89$ by observations, we derive the Noether conditions for the vector field in quintessence, phantom and quintom models, respectively. In the first two cases, constant potential solutions have been obtained. What is more, a fast decaying point-like solution with power-law potential is also found for the vector field in quintessence model. For the quintom case, we find an interesting constraint $\tilde{C}V_{p}'=-CV_{q}'$ on the field potentials, where $C$ and $\tilde{C}$ are constants related to the Noether symmetry.