Loop quantum modified gravity and its cosmological application

Abstract

A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical framework of these theories is rigorously constructed. Both the Hamiltonian and master constraint operators are well defined and proposed to represent quantum dynamics of scalar-tensor theories. As an application to models, we set up the basic structure of loop quantum Brans-Dicke cosmology. The effective dynamical equations of loop quantum Brans-Dicke cosmology are also obtained, which lay a foundation for the phenomenological investigation to possible quantum gravity effects in cosmology.

18pages. arXiv admin note: substantial text overlap with arXiv:1107.5157

References in corpus (40)

• f(R) Theories Of Gravity
• Quantum Gravity at a Lifshitz Point
• Background Independent Quantum Gravity: A Status Report
• Dark Energy and the Accelerating Universe
• The Confrontation between General Relativity and Experiment
• Discreteness of area and volume in quantum gravity
• Loop Quantum Cosmology: A Status Report
• Quantum Nature of the Big Bang: Improved dynamics
• Reconstruction of a scalar-tensor theory of gravity in an accelerating universe
• Real Ashtekar Variables for Lorentzian Signature Space-times
• Runaway dilaton and equivalence principle violations
• Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field
• Fundamental Structure of Loop Quantum Gravity
• Critical Gravity in Four Dimensions
• Cosmic acceleration without quintessence
• The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity
• Loop Quantum Cosmology: An Overview
• A length operator for canonical quantum gravity
• Alternative quantization of the Hamiltonian in loop quantum cosmology II: Including the Lorentz term
• Dark Matter Relic Abundance and Scalar-Tensor Dark Energy
• Polymer and Fock representations for a Scalar field
• 5-dimensional Brans-Dicke Theory and Cosmic Acceleration
• Hamiltonian Formulation of Palatini f(R) theories a la Brans-Dicke
• Extension of loop quantum gravity to $f(R)$ theories
• Path Integrals and the WKB approximation in Loop Quantum Cosmology
• High-order quantum back-reaction and quantum cosmology with a positive cosmological constant
• New length operator for loop quantum gravity
• Nonperturbative Loop Quantization of Scalar-Tensor Theories of Gravity
• Loop quantum $f(R)$ theories
• Effective Scenario of Loop Quantum Cosmology
• Master Constraint Operator in Loop Quantum Gravity
• Loop quantum Brans-Dicke cosmology
• Exact cosmological solution of a Scalar-Tensor Gravity theory compatible with the $\Lambda CDM$ model
• Brans-Dicke Scalar Field as a Unique k-essence
• Coherent State Functional Integral in Loop Quantum Cosmology: Alternative Dynamics
• Loop Quantum Brans-Dicke Theory
• Path Integrals and Alternative Effective Dynamics in Loop Quantum Cosmology
• Dynamics of Scalar Field in Polymer-like Representation
• Coherent State Functional Integrals in Quantum Cosmology
• Extension of Loop Quantum Gravity to Metric Theories beyond General Relativity

Cited by in corpus (9)

• On $R+\alpha R^2$ Loop Quantum Cosmology
• Bounce Loop Quantum Cosmology Corrected Gauss-Bonnet Gravity
• A comparison between Jordan and Einstein frames of Brans-Dicke gravity a la loop quantum cosmology
• Pre-inflationary dynamics of Starobinsky inflation and its generization in Loop Quantum Brans-Dicke Cosmology
• How can holonomy corrections be introduced in $f(R)$ gravity?
• Connection Dynamics for Higher Dimensional Scalar-Tensor Theories of Gravity
• 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
• Mechanics of Isolated Horizons in Scalar-Tensor Theories