A study of phantom scalar field cosmology using Lie and Noether symmetries

Abstract

The paper deals with phantom scalar field cosmology in Einstein gravity. At first using Lie symmetry, the coupling function to the kinetic term and the potential function of the scalar field and the equation of state parameter of the matter field are determined and a simple solution is obtained. Subsequently, Noether symmetry is imposed on the Lagrangian of the system. The symmetry vector is obtained and the potential takes a very general form from which potential using Lie Symmetry can be obtained as a particular case. Then we choose a point transformation $(a,\varphi )\to (u,v)$ such that one of the transformed variables (say u) is a cyclic for the Lagrangian. Using conserved charge (corresponding to the cyclic coordinate) and the constant of motion, solutions are obtained.

14 pages, 9 figures, accepted for publication in Int. J. Mod. Phys. D (2016)

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• New exact and analytic solutions in Weyl Integrable cosmology from Noether symmetry analysis
• Variable $G$ and $\Lambda$ gravity theory and analytical Cosmological Solutions using Noether symmetry approach
• On the necessity of phantom fields for solving the horizon problem in scalar cosmologies
• Answer to the Comments on the paper "A study of phantom scalar field cosmology using Lie and Noether symmetries" by A. Paliathanasis, et al. arXiv:1605.05147
• Classical and quantum cosmology in $f(T)$-gravity theory: A Noether symmetry approach
• Comment on "A study of phantom scalar field cosmology using Lie and Noether symmetries" [Int. J. Mod. Phys. D 25 (2016) 1650051]