Quintom cosmological model and some possible solutions using Lie and Noether symmetries
Abstract
The present work deals with a quintom model of dark energy in the framework of a spatially flat isotropic and homogeneous Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. At first, Lie point symmetry is imposed to the system and the unknown coupled potential of the model is determined. Then Noether symmetry, which is also a point like symmetry of the Lagrangian, is imposed on the physical system and the potential takes a general form. It is shown that the Lie algebra of Noether symmetry is a sub-algebra of the corresponding Lie algebra of the Lie symmetry. Finally, a point transformation in the three dimensional augmented space is performed suitably so that one of the variables become cyclic and as a result there is considerable simplification to the physical system. Hence conserved quantities (i.e, constants of motion) are expressed in a compact form and cosmological solutions are evaluated and analyzed in the present context.
Cite
@article{arxiv.1607.03396,
title = {Quintom cosmological model and some possible solutions using Lie and Noether symmetries},
author = {Sourav Dutta and Muthusamy Lakshmanan and Subenoy Chakraborty},
journal= {arXiv preprint arXiv:1607.03396},
year = {2016}
}
Comments
14 pages, 6 figures, accepted in IJMPD