Noether symmetric classical and quantum scalar field cosmology

Abstract

We study the evolution of a two dimensional minisuperspace cosmological model in classical and quantum levels by the Noether symmetry approach. The phase space variables turn out to correspond to the scale factor of a Friedmann-Robertson-Walker (FRW) model and a scalar field with which the action of the model is augmented. It is shown that the minisuperspace of such a model is a two dimensional manifold with vanishing Ricci scalar. We present a coordinate transformation which cast the corresponding minisuper metric to a Minkowskian or Euclidean one according to the choices of an ordinary or phantom model for the scalar field. Then, the Noether symmetry of such a cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generators of the desired symmetry. We explicitly calculate the form of the scalar field potential functions for which such symmetries exist. For these potential functions, the exact classical and quantum solutions in the cases where the scalar field is an ordinary or a phantom one, are presented and compared.

18 pages, 13 figures, revised version, to appear in CQG

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• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach
• Quantum phantom cosmology
• Using the Noether symmetry approach to probe the nature of dark energy
• Noether Symmetry Approach in f(R) Tachyon Model
• Noether symmetry in $f(R)$ cosmology
• Two dimensional dynamical systems which admit Lie and Noether symmetries
• Bianchi spacetimes in noncommutative phase-space
• Evolutionary quantum cosmology in a gauge-fixed picture

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