Using the Noether symmetry approach to probe the nature of dark energy

Abstract

We propose to use a model-independent criterion based on first integrals of motion, due to Noether symmetries of the equations of motion, in order to classify the dark energy models in the context of scalar field (quintessence or phantom) FLRW cosmologies. In general, the Noether symmetries play an important role in physics because they can be used to simplify a given system of differential equations as well as to determine the integrability of the system. The Noether symmetries are computed for nine distinct accelerating cosmological scenarios that contain a homogeneous scalar field associated with different types of potentials. We verify that all the scalar field potentials, presented here, admit the trivial first integral namely energy conservation, as they should. We also find that the exponential potential inspired from scalar field cosmology, as well as some types of hyperbolic potentials, include extra Noether symmetries. This feature suggests that these potentials should be preferred along the hierarchy of scalar field potentials. Finally, using the latter potentials, in the framework of either quintessence or phantom scalar field cosmologies that contain also a non-relativistic matter(dark matter) component, we find that the main cosmological functions, such as the scale factor of the universe, the scalar field, the Hubble expansion rate and the metric of the FRLW space-time, are computed analytically. Interestingly, under specific circumstances the predictions of the exponential and hyperbolic scalar field models are equivalent to those of the $\Lambda$CDM model, as far as the global dynamics and the evolution of the scalar field are concerned. The present analysis suggests that our technique appears to be very competitive to other independent tests used to probe the functional form of a given potential and thus the associated nature of dark energy.

Accepted for publication in Physical Review D (13 pages)

References in corpus (20)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Dynamics of dark energy
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results
• Improved Cosmological Constraints from New, Old and Combined Supernova Datasets
• Improved Dark Energy Constraints from ~100 New CfA Supernova Type Ia Light Curves
• WMAP constraints on low redshift evolution of dark energy
• Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach
• Mapping the Cosmological Expansion
• LXCDM: a cosmon model solution to the cosmological coincidence problem?
• Dark energy as a massive vector field
• Unified Dark Matter in Scalar Field Cosmologies
• Noether symmetry in $f(R)$ cosmology
• Lie and Noether symmetries of geodesic equations and collineations
• The generalized second law in phantom dominated universes in the presence of black holes
• Two dimensional dynamical systems which admit Lie and Noether symmetries
• The spherical collapse model and cluster formation beyond the $\Lambda$ cosmology: Indications for a clustered dark energy?
• Determining Cosmological Parameters with Latest Observational Data
• Probing Dynamics of Dark Energy with Supernova, Galaxy Clustering and the Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations
• Dark-Energy Dynamics Required to Solve the Cosmic Coincidence

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