Diffeomorphism invariant cosmological sector in loop quantum gravity
arXiv:1706.02424 · doi:10.1088/1361-6382/aa89c6
Abstract
In this paper we work out in detail a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, and propose how to compare in detail the physics of this sector with that of loop quantum cosmology. The key technical steps we have completed are (a) to formulate conditions for homogeneity and isotropy in a diffeomorphism covariant way on the classical phase space of general relativity, and (b) to translate these conditions consistently using well-understood techniques to loop quantum gravity. To impose the symmetry at the quantum level, on both the connection and its conjugate momentum, the method used necessarily has similiarities to the Gupta-Bleuler method of quantizing the electromagnetic field. Lastly, a strategy for embedding states of loop quantum cosmology into this new homogeneous isotropic sector, and using this embedding to compare the physics, is presented.
25 pages
References in corpus (47)
- Background Independent Quantum Gravity: A Status Report
- Discreteness of area and volume in quantum gravity
- Loop Quantum Cosmology: A Status Report
- Quantum Nature of the Big Bang: Improved dynamics
- Quantum Theory of Gravity I: Area Operators
- Quantum Nature of the Big Bang
- Real Ashtekar Variables for Lorentzian Signature Space-times
- Quantum Spin Dynamics (QSD)
- Black hole entropy in Loop Quantum Gravity
- Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
- Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
- Real and complex connections for canonical gravity
- Loop quantum cosmology of k=1 FRW models
- Representations of the holonomy algebras of gravity and non-Abelian gauge theories
- Differential Geometry on the Space of Connections via Graphs and Projective Limits
- Loop quantum cosmology of Bianchi I models
- Quantum gravity, shadow states, and quantum mechanics
- A Quantum Gravity Extension of the Inflationary Scenario
- The physical hamiltonian in nonperturbative quantum gravity
- An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era
- Loop quantum cosmology of Bianchi type IX models
- Loop quantum cosmology and the k = - 1 RW model
- Black hole entropy from an SU(2)-invariant formulation of Type I isolated horizons
- Closed FRW model in Loop Quantum Cosmology
- Introduction to Loop Quantum Cosmology
- Is loop quantization in cosmology unique?
- Complexifier Coherent States for Quantum General Relativity
- Casting Loop Quantum Cosmology in the Spin Foam Paradigm
- Loop Quantum Cosmology and Spin Foams
- The SU(2) Black Hole entropy revisited
- Consistency Check on Volume and Triad Operator Quantisation in Loop Quantum Gravity II
- Consistency Check on Volume and Triad Operator Quantisation in Loop Quantum Gravity I
- Path Integrals and the WKB approximation in Loop Quantum Cosmology
- Separable Hilbert space in Loop Quantum Gravity
- Quantum gravity and the standard model
- Prescriptions in Loop Quantum Cosmology: A comparative analysis
- The combinatorics of the SU(2) black hole entropy in loop quantum gravity
- Relating loop quantum cosmology to loop quantum gravity: Symmetric sectors and embeddings
- A spin-foam vertex amplitude with the correct semiclassical limit
- Local spinfoam expansion in loop quantum cosmology
- Quantum field theory and its symmetry reduction
- Vertex Expansion for the Bianchi I model
- Uniqueness of the Representation in Homogeneous Isotropic LQC
- Loop Quantum Cosmology
- Diffeomorphism invariant cosmological symmetry in full quantum gravity
- Kinematical uniqueness of homogeneous isotropic LQC
- Approximating the physical inner product of Loop Quantum Cosmology
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- Dapor-Liegener formalism of loop quantum cosmology for Bianchi I spacetimes
- Universal properties of the evolution of the Universe in modified loop quantum cosmology
- Quantum isotropy and the reduction of dynamics in Bianchi I
- Cosmology in Loop Quantum Gravity: symmetry reduction preserving gauge degrees of freedom