Noether Symmetry Approach in "Cosmic Triad" Vector Field Scenario

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 $-1.21\le \omega \le -0.89$ 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 $\tilde{C}{V}_p^{\prime }=-C{V}_q^{\prime }$ on the field potentials, where $C$ and $\tilde{C}$ are constants related to the Noether symmetry.

15 pages, no figures, accepted by Classical and Quantum Gravity.

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Cited by in corpus (9)

• Non-Abelian Gauge Field Inflation
• Noether Symmetry in $f(T)$ Theory
• Fermion field as inflaton, dark energy and dark matter
• Revisiting the dynamics of interacting vector-like dark energy
• Exact Cosmological Solutions of $f(R)$ Theories via Hojman Symmetry
• Hojman Symmetry in $f(T)$ Theory
• The Unified First law in "Cosmic Triad" Vector Field Scenario
• Conformal coupling associated with the Noether symmetry and its connection with the $\Lambda$CDM dynamics
• Power-law Bianchi type I inflation with multiple vector fields