Hamiltonian dynamics and Noether symmetries in Extended Gravity Cosmology

Abstract

We discuss the Hamiltonian dynamics for cosmologies coming from Extended Theories of Gravity. In particular, minisuperspace models are taken into account searching for Noether symmetries. The existence of conserved quantities gives selection rule to recover classical behaviors in cosmic evolution according to the so called Hartle criterion, that allows to select correlated regions in the configuration space of dynamical variables. We show that such a statement works for general classes of Extended Theories of Gravity and is conformally preserved. Furthermore, the presence of Noether symmetries allows a straightforward classification of singularities that represent the points where the symmetry is broken. Examples of nonminimally coupled and higher-order models are discussed.

20 pages, Review paper to appear in EPJC

References in corpus (6)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Low surface brightness galaxies rotation curves in the low energy limit of $R^n$ gravity : no need for dark matter?
• Dark energy from modified gravity with Lagrange multipliers
• Classifying and avoiding singularities in the alternative gravity dark energy models
• Theory of gravitation theories: a no-progress report

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