Three fluid cosmological model using Lie and Noether symmetries

Abstract

We employ a three fluid model in order to construct a cosmological model in the Friedmann Robertson Walker flat spacetime, which contains three types of matter dark energy, dark matter and a perfect fluid with a linear equation of state. Dark matter is described by dust and dark energy with a scalar field with potential V(ϕ). In order to fix the scalar field potential we demand Lie symmetry invariance of the field equations, which is a model-independent assumption. The requirement of an extra Lie symmetry selects the exponential scalar field potential. The further requirement that the analytic solution is invariant under the point transformation generated by the Lie symmetry eliminates dark matter and leads to a quintessence and a phantom cosmological model containing a perfect fluid and a scalar field. Next we assume that the Lagrangian of the system admits an extra Noether symmetry. This new assumption selects the scalar field potential to be exponential and forces the perfect fluid to be stiff. Furthermore the existence of the Noether integral allows for the integration of the dynamical equations. We find new analytic solutions to quintessence and phantom cosmologies which contain all three fluids. Using these solutions one is able to compute analytically all main cosmological functions, such as the scale factor, the scalar field, the Hubble expansion rate, the deceleration parameter etc.

accepted for publication in Class. Quantum Grav. (12 pages)

References in corpus (8)

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• Using the Noether symmetry approach to probe the nature of dark energy
• Noether Symmetry Approach in f(R) Tachyon Model
• Unified Dark Matter in Scalar Field Cosmologies
• Noether symmetry in $f(R)$ cosmology
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• A study of phantom scalar field cosmology using Lie and Noether symmetries
• Dirac field as a source of the inflation in 2+1 dimensional Teleparallel gravity
• Phase-space analysis of the cosmological 3-fluid problem: Families of attractors and repellers
• Exact Cosmological Solutions of $f(R)$ Theories via Hojman Symmetry
• Quantum cosmology with symmetry analysis for quintom dark energy model
• Generalized Model of Interacting Dark Energy and Dark Matter : Phase Portrait Analysis of Evolving Universe
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• Classical and Quantum Cosmology in Einstein-aether Scalar-tensor gravity: Noether Symmetry Analysis
• Quantum Cosmology in Coupled Brans-Dicke Gravity: A Noether Symmetry Analysis
• Dynamical System Analysis of a Three Fluid Cosmological Model : An Invariant Manifold approach
• Numerical solutions to the cosmological 3-fluid problem
• Comment on "A study of phantom scalar field cosmology using Lie and Noether symmetries" [Int. J. Mod. Phys. D 25 (2016) 1650051]