Using Noether symmetries to specify f(R) gravity

Abstract

A detailed study of the modified gravity, f(R) models is performed, using that the Noether point symmetries of these models are geometric symmetries of the mini superspace of the theory. It is shown that the requirement that the field equations admit Noether point symmetries selects definite models in a self-consistent way. As an application in Cosmology we consider the Friedman -Robertson-Walker spacetime and show that the only cosmological model which is integrable via Noether point symmetries is the $(R^b-2\Lambda {)}^c$ model, which generalizes the Lambda Cosmology. Furthermore using the corresponding Noether integrals we compute the analytic form of the main cosmological functions.

16 pages, no figures, Talk given at the 15th Conference on Recent Developments in Gravity (NEB XV), 20-23 June 2012, Chania, Greece

References in corpus (15)

• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Disappearing cosmological constant in f(R) gravity
• Conditions for the cosmological viability of f(R) dark energy models
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Are f(R) dark energy models cosmologically viable ?
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach
• Using the Noether symmetry approach to probe the nature of dark energy
• Power-laws f(R) theories are cosmologically unacceptable
• Noether symmetry in $f(R)$ cosmology
• Two dimensional dynamical systems which admit Lie and Noether symmetries
• Generalizing the autonomous Kepler Ermakov system in a Riemannian space
• Noether symmetry approach in matter-dominated cosmology with variable G and Lambda
• Revisiting Noether gauge symmetry for F(R) theory of gravity
• Revisit emission spectrum and entropy quantum of the Reissner-Nordström black hole

Cited by in corpus (7)

• Noether symmetries and analytical solutions in f(T)-cosmology: A complete study
• Invariant solutions and Noether symmetries in Hybrid Gravity
• Updating constraints on f(T) teleparallel cosmology and the consistency with Big Bang Nucleosynthesis
• Classical and Quantum Solutions in Brans-Dicke Cosmology with a Perfect Fluid
• Analytical solutions in $R+q{R}^n$ cosmology from singularity analysis
• Noether symmetries and duality transformations in cosmology
• Cosmological Solutions for the Geometrical Scalar-Tensor with the Potential Determined by the Noether Symmetry Approach