$f(R)$-gravity from Killing Tensors

Abstract

We consider $f\left(R\right)$-gravity in a Friedmann-Lemaître-Robertson-Walker spacetime with zero spatial curvature. We apply the Killing tensors of the minisuperspace in order to specify the functional form of $f\left(R\right)$ and the field equations to be invariant under Lie-Bäcklund transformations which are linear in the momentum (contact symmetries). Consequently, the field equations to admit quadratic conservation laws given by Noether's Theorem. We find three new integrable $f\left(R\right)$ models, for which with the application of the conservation laws we reduce the field equations to a system of two first-order ordinary differential equations. For each model we study the evolution of the cosmological fluid. Where we find that for the one integrable model the cosmological fluid has an equation of state parameter, in which in the latter there is a linear behavior in terms of the scale factor which describes the Chevallier, Polarski and Linder (CPL) parametric dark energy model.

20 pages, 4 figures, minor corrections, to appear in Classical and Quantum Gravity

References in corpus (23)

• Dynamics of dark energy
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Improved Cosmological Constraints from New, Old and Combined Supernova Datasets
• Modified teleparallel gravity: inflation without inflaton
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• On Born-Infeld Gravity in Weitzenbock spacetime
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• The 1% Concordance Hubble Constant
• String-inspired Gauss-Bonnet gravity reconstructed from the universe expansion history and yielding the transition from matter dominance to dark energy
• Dark energy from modified gravity with Lagrange multipliers
• Using the Noether symmetry approach to probe the nature of dark energy
• Two scalar field cosmology: Conservation laws and exact solutions
• Gravity and Scalar Fields
• Scalar-Tensor Gravity Cosmology: Noether symmetries and analytical solutions
• Gauss-Bonnet dark energy by Lagrange multipliers
• Dynamical symmetries and observational constraints in scalar field cosmology
• Noether analysis of Scalar-Tensor Cosmology
• Hyperbolic Inflation in the Light of Planck 2015 data
• Cosmological tests of modified gravity: constraints on $F(R)$ theories from the galaxy clustering ratio
• Canonical Quantization of the BTZ Black Hole using Noether Symmetries
• On analytical solutions of f(R) modified gravity theories in FLRW cosmologies

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