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

Spyros Basilakos, Michael Tsamparlis, and Andronikos Paliathanasis
Phys. Rev. D 83, 103512 – Published 9 May 2011

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) Friedmann-Lemaître-Robertson-Walker 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 nonrelativistic 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 Friedmann-Lemaître-Robertson-Walker 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 ΛCDM 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.

  • Received 24 February 2011

DOI:https://doi.org/10.1103/PhysRevD.83.103512

© 2011 American Physical Society

Authors & Affiliations

Spyros Basilakos1, Michael Tsamparlis2, and Andronikos Paliathanasis2

  • 1Academy of Athens, Research Center for Astronomy and Applied Mathematics, Soranou Efesiou 4, 11527, Athens, Greece
  • 2Faculty of Physics, Department of Astrophysics - Astronomy - Mechanics, University of Athens, Panepistemiopolis, Athens 157 83, Greece

See Also

Constraints and analytical solutions of f(R) theories of gravity using Noether symmetries

Andronikos Paliathanasis, Michael Tsamparlis, and Spyros Basilakos
Phys. Rev. D 84, 123514 (2011)

Scalar-tensor gravity cosmology: Noether symmetries and analytical solutions

Andronikos Paliathanasis, Michael Tsamparlis, Spyros Basilakos, and Salvatore Capozziello
Phys. Rev. D 89, 063532 (2014)

Two scalar field cosmology: Conservation laws and exact solutions

Andronikos Paliathanasis and Michael Tsamparlis
Phys. Rev. D 90, 043529 (2014)

Dynamical symmetries and observational constraints in scalar field cosmology

Andronikos Paliathanasis, Michael Tsamparlis, and Spyros Basilakos
Phys. Rev. D 90, 103524 (2014)

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Vol. 83, Iss. 10 — 15 May 2011

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