Noether symmetric $f(R)$ quantum cosmology and its classical correlations

Abstract

We quantize a flat FRW cosmology in the context of the $f(R)$ gravity by Noether symmetry approach. We explicitly calculate the form of $f(R)$ for which such symmetries exist. It is shown that the existence of a Noether symmetry yields a general solution of the Wheeler-DeWitt equation where can be expressed as a superposition of states of the form $e^{iS}$. In terms of Hartle criterion, this type of wave function exhibits classical correlations, i.e. the emergent of classical universe is expected due to the oscillating behavior of the solutions of Wheeler-DeWitt equation. According to this interpretation we also provide the Noether symmetric classical solutions of our $f(R)$ cosmological model.

11 pages, 1 figure, to appear in PLB

References in corpus (51)

• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Curvature Quintessence
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Cosmology on a Brane in Minkowski Bulk
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• 1/R gravity and Scalar-Tensor Gravity
• Modified f(R) gravity unifying R^m inflation with \LambdaCDM epoch
• One-loop f(R) gravity in de Sitter universe
• On Physical Equivalence between Nonlinear Gravity Theories
• Dark energy cosmology from higher-order, string-inspired gravity and its reconstruction
• Where new gravitational physics comes from: M-theory?
• 1/R Curvature Corrections as the Source of the Cosmological Acceleration
• The Power of General Relativity
• Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach
• Metric-affine f(R) theories of gravity
• Consistent modified gravity: dark energy, acceleration and the absence of cosmic doomsday
• Palatini form of 1/R gravity
• Higher order gravity theories and scalar tensor theories
• Newton law corrections and instabilities in $f(R)$ gravity with the effective cosmological constant epoch
• Cosmological Evolution in 1/R-Gravity Theory
• Modified Friedmann Equations in R${}^{-1}$-Modified Gravity
• Palatini Formulation of Modified Gravity with $\ln R$ Terms
• The phase space view of f(R) gravity
• Dark energy, inflation and dark matter from modified F(R) gravity
• Noether symmetry in $f(R)$ cosmology
• Noether symmetries in Bianchi universes
• Selection Rules in Minisuperspace Quantum Cosmology
• Spherically Symmetric Solutions to Fourth-Order Theories of Gravity
• Some Observational Consequences of Brane World Cosmologies
• Exact cosmological solutions of scale-invariant gravity theories
• Reconstruction of the Scalar-Tensor Lagrangian from a LCDM Background and Noether Symmetry
• Noether symmetry in the higher order gravity theory
• Bianchi spacetimes in noncommutative phase-space
• Palatini f(R) gravity and Noether symmetry
• Acceleration of the universe in the Einstein frame of a metric-affine f(R) gravity
• Palatini formulation of the $R^{-1}$modified gravity with an additionally squared scalar curvature term
• Noether and some other dynamical symmetries in Kantowski-Sachs model
• One-loop f(R) Gravitational Modified Models
• Is Noether Symmetric Approach Consistent With Dynamical Equation In Non-minimal Scalar-Tensor Theories?
• Quantum cosmology with a curvature squared action
• Quantum Cosmology With R+R^2 Gravity
• Accelerated expansion in modified gravity with a Yukawa-like term
• A Note on the Semi-Classical Approximation in Quantum Gravity
• Palatini formulation of modified gravity with squared scalar curvature
• Noether symmetry approach in matter-dominated cosmology with variable G and Lambda
• f(R) Quantum Cosmology

Cited by in corpus (52)

• f(R) theories
• Noether Symmetry in $f(T)$ Theory
• Noether Symmetry Approach in f(R) Tachyon Model
• $f(T)$ cosmology via Noether symmetry
• Initial and final de Sitter universes from modified $f(R)$ gravity
• Dynamical analysis in scalar field cosmology
• Noether symmetry of F(T) cosmology with quintessence and phantom scalar fields
• Two scalar field cosmology: Conservation laws and exact solutions
• Bianchi Type I Cosmology in Generalized Saez-Ballester Theory via Noether Gauge Symmetry
• Noether Gauge Symmetry Approach in f(R) Gravity
• Invariant solutions and Noether symmetries in Hybrid Gravity
• Quadratic quantum cosmology with Schutz' perfect fluid
• Dynamical symmetries and observational constraints in scalar field cosmology
• FLRW metric $f(R)$ cosmology with a perfect fluid by generating integrals of motion
• The geometric origin of Lie point symmetries of the Schrödinger and the Klein Gordon equations
• Exact cosmological solutions from Hojman conservation quantities
• Noether symmetric classical and quantum scalar field cosmology
• The distinctions between $\Lambda$CDM and $f(T)$ gravity according Noether symmetry
• Generalized (2+1) dimensional black hole by Noether symmetry
• Towards the Quantization of Eddington-inspired-Born-Infeld Theory
• Viability of Noether symmetry of F(R) theory of gravity
• Noether symmetry in $f(T)$ teleparallel gravity
• Modified theory of gravity and the history of cosmic evolution
• Revisiting Noether gauge symmetry for F(R) theory of gravity
• Quantization of the Schwarzschild black hole: a Noether symmetry approach
• Why Noether symmetry of F(R) theory yields three-half power law?
• Noether symmetric minisuperspace model of $f(R)$ cosmology
• Studying the Intervention of an Unusual Term in $f(T)$ Gravity via Noether Symmetry
• Revisiting conserved currents in F(R) theory of gravity via Noether symmetry
• Noether Symmetries of a Modified Model in Teleparallel Gravity and a New Approach for Exact Solutions
• Minisuperspace Quantization of $f\left(T,B\right)$ Cosmology
• Wheeler-DeWitt equation and Lie symmetries in Bianchi scalar-field cosmology
• Hojman Symmetry Approach for Scalar-Tensor Cosmology
• Similarity solutions for the Wheeler-DeWitt equation in $f\left(R\right)$-cosmology
• On the equivalence between different canonical forms of F(R) theory of gravity
• Third quantization of $f(R)$-type gravity II - General $f(R)$ case -
• f(T) Quantum Cosmology
• Field independent cosmic evolution
• Exact solution of the Einstein-Skyrme model in a Kantowski-Sachs spacetime
• Late-time-accelerated expansion arisen from gauge fields in an anisotropic background and a fruitful trick for Noether's approach
• Three-dimensional black holes via Noether symmetries
• Quadratic integrals of a multi-scalar cosmological model
• Symmetries of Differential equations and Applications in Relativistic Physics
• Closed-form solutions of the Wheeler-DeWitt equation in a scalar-vector field cosmological model by Lie symmetries
• Reconstructing modified and alternative theories of gravity
• (2+1)-dimensional f(R) gravity solutions via Hojman symmetry
• Some aspects of modified theory of gravity in Palatini formalism unveiled
• Analyzing Conserved Currents in F(R) theory of gravity
• Quantum cosmology in teleparallel gravity with a boundary term
• Noether gauge symmetry approach applying for the non-minimally coupled gravity to the Maxwell field
• Generalized Noether Theorem for Gauss-Bonnet Cosmology
• Extended Theories of Gravity in cosmological and astrophysical applications