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.

14 pages, 6 figures, accepted in IJMPD

References in corpus (14)

• Dynamics of dark energy
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Reconstructing Dark Energy
• Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach
• Theoretical Models of Dark Energy
• Generalized Second Law of Thermodynamics in Quintom Dominated Universe
• Constraints on the Sound Speed of Dynamical Dark Energy
• Noether symmetry in $f(R)$ cosmology
• Lie and Noether symmetries of geodesic equations and collineations
• Shape invariance method for quintom model in the bent brane background
• Two dimensional dynamical systems which admit Lie and Noether symmetries
• Equivalence between Palatini and metric formalisms of f(R)-gravity by divergence free current
• Probing Dynamics of Dark Energy with Supernova, Galaxy Clustering and the Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations
• Probing Inflation and Dark Energy with Current Cosmological Observations