Loop quantum $f(R)$ theories

Abstract

As modified gravity theories, the 4-dimensional metric $f(R)$ theories are cast into connection dynamical formalism with real $su(2)$-connections as configuration variables. This formalism enables us to extend the non-perturbative loop quantization scheme of general relativity to any metric $f(R)$ theories. The quantum kinematical framework of $f(R)$ gravity is rigorously constructed, where the quantum dynamics can be launched. Both Hamiltonian constraint operator and master constraint operator for $f(R)$ theories are well defined. Our results show that the non-perturbative quantization procedure of loop quantum gravity are valid not only for general relativity but also for a rather general class of 4-dimensional metric theories of gravity.

14 pages; published version in PRD

References in corpus (8)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Dark Energy and the Accelerating Universe
• Gravity quantized
• Are the spectra of geometrical operators in Loop Quantum Gravity really discrete?
• Extension of loop quantum gravity to $f(R)$ theories
• New length operator for loop quantum gravity
• Various Hamiltonian formulations of f(R) gravity and their canonical relationships
• Extended Loop Quantum Gravity

Cited by in corpus (49)

• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Shadow and stability of quantum-corrected black holes
• Quantum Gravity in the Sky: Interplay between fundamental theory and observations
• Phenomenological investigation of a quantum gravity extension of inflation with the Starobinsky potential
• On $R+\alpha R^2$ Loop Quantum Cosmology
• Nonperturbative Loop Quantization of Scalar-Tensor Theories of Gravity
• Bounce Loop Quantum Cosmology Corrected Gauss-Bonnet Gravity
• Non-singular Bounce Cosmology from Lagrange Multiplier $F(R)$ Gravity
• Loop quantum black hole
• Binary Black Hole merger in f(R) theory
• Singular $F(R)$ Cosmology Unifying Early and Late-time Acceleration with Matter and Radiation Domination Era
• A comparison between Jordan and Einstein frames of Brans-Dicke gravity a la loop quantum cosmology
• Loop quantum Brans-Dicke cosmology
• The no-boundary measure in scalar-tensor gravity
• Loop Quantum Brans-Dicke Theory
• Pre-inflationary dynamics of Starobinsky inflation and its generization in Loop Quantum Brans-Dicke Cosmology
• Inflation from non-minimally coupled scalar field in loop quantum cosmology
• The effective dynamics of loop quantum $R^2$ cosmology
• Shadows and optical appearance of quantum-corrected black holes illuminated by static thin accretions
• Background dynamics of pre-inflationary scenario in Brans-Dicke loop quantum cosmology
• How can holonomy corrections be introduced in $f(R)$ gravity?
• Generalized Ashtekar variables for Palatini f(R) models
• Quasi-normal Modes of Static Spherically Symmetric Black Holes in $f(R)$ Theory
• Symmetry Reduced Loop Quantum Gravity: A Bird's Eye View
• Loop quantum gravity and cosmological constant
• (3+1)-Formulation for Gravity with Torsion and Non-Metricity: The Stress-Energy-Momentum Equation
• Distinguishing f(R) theories from general relativity by gravitational lensing effect
• Viable non-singular cosmic bounce in holonomy improved F(R) gravity endowed with a Lagrange multiplier
• Non-Gaussian features from the inverse volume corrections in loop quantum cosmology
• Extension of Loop Quantum Gravity to Metric Theories beyond General Relativity
• Canonical loop quantization of the lowest-order projectable Horava gravity
• Consistency check on the fundamental and alternative flux operators in loop quantum gravity
• Loop quantum modified gravity and its cosmological application
• (3+1)-Formulation for Gravity with Torsion and Non-Metricity II: The Hypermomentum Equation
• Connection Dynamics for Higher Dimensional Scalar-Tensor Theories of Gravity
• Loop Quantum Cosmology Scalar Field Models
• Anamorphic Quasiperiodic Universes in Modified and Einstein Gravity with Loop Quantum Gravity Corrections
• Loop quantum cosmology from an alternative Hamiltonian. II. Including the Lorentzian term
• Shape Dynamical Loop Gravity from a Conformal Immirzi Parameter
• Loop quantum cosmological dynamics of scalar-tensor theory in the Jordan frame
• Alternative $k=-1$ loop quantum cosmology
• Loop Quantum Vector-Tensor Gravity and Its Spherically Symmetric Model
• Conformally Invariant Brans-Dicke Loop Quantum Cosmology: A Quantum Geometric Model of Linking Theory
• Connection Dynamics of Reduced 5-dimensional Kaluza-Klein Theory and Its Deparametrization
• Realization of Dirac quantization in loop quantum gravity
• Degenerate Limits of Scalar-Tensor Gravity
• Connection dynamics of a gauge theory of gravity coupled with matter
• Mechanics of Isolated Horizons in Scalar-Tensor Theories
• Hamiltonian Theory: generalizations to higher dimensions, supersymmetry and modified gravity