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 (36)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Dynamics of dark energy
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• The Cosmological Constant and Dark Energy
• Cosmological Imprint of an Energy Component with General Equation of State
• A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state
• Cosmological Constant - the Weight of the Vacuum
• The Case for a Positive Cosmological Lambda-term
• The Cosmological Constant
• Properties of singularities in (phantom) dark energy universe
• Planck 2013 results. XXII. Constraints on inflation
• Quintom Cosmology: Theoretical implications and observations
• Reconstructing Dark Energy
• Constraints on Cosmological Models from Hubble Space Telescope Observations of High-z Supernovae
• Cross-correlation Tomography: Measuring Dark Energy Evolution with Weak Lensing
• Oscillating Quintom and the Recurrent Universe
• Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach
• Theoretical Models of Dark Energy
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological implications of the large-scale two-point correlation function
• Generalized Second Law of Thermodynamics in Quintom Dominated Universe
• f(R) cosmology by Noether's symmetry
• Dark Energy: the Cosmological Challenge of the Millennium
• Constraints on Oscillating Quintom from Supernova, Microwave Background and Galaxy Clustering
• Constraints on the Sound Speed of Dynamical Dark Energy
• Noether symmetry approach in phantom quintessence cosmology
• 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
• Reconstruction of the Scalar-Tensor Lagrangian from a LCDM Background and Noether Symmetry
• Two dimensional dynamical systems which admit Lie and Noether symmetries
• Noether Symmetry Approach in multiple scalar fields Scenario
• 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
• Equation of state for Universe from similarity symmetries
• Probing Inflation and Dark Energy with Current Cosmological Observations

Cited by in corpus (6)

• Dynamical system analysis of Quintom Dark Energy Model
• Multi-fluid cosmology in Einstein gravity: analytical solutions
• Dynamical description of a quintom cosmological model nonminimally coupled with gravity
• Quantum cosmology for non-minimally coupled scalar field in FLRW space-time: A symmetry analysis
• Noether Symmetry analysis in Chameleon Field Cosmology
• Classical and quantum cosmology in $f(T)$-gravity theory: A Noether symmetry approach