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Mathematical structure of loop quantum cosmology
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Mathematical structure of loop quantum cosmology
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Applications of Riemannian quantum geometry to cosmology have had notable successes. In particular, the fundamental discreteness underlying quantum geometry has led to a natural resolution of the big bang singularity. However, the precise mathematical structure underlying loop quantum cosmology and the sense in which it implements the full quantization program in a symmetry reduced model has not been made explicit. The purpose of this paper is to address these issues, thereby providing a firmer mathematical and conceptual foundation to the subject.
Forward citations
Cited by 13 Pith papers
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Prism Effect in Quantum Gravity
Electromagnetic backreaction on quantum geometry in LQC makes the photon group velocity mode-dependent and subluminal, a 'prism effect' that vanishes at low energies.
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Quantum Cosmological Backreactions III: Deparametrised Quantum Cosmological Perturbation Theory
Backreactions from inhomogeneous modes on homogeneous geometry are significant and sensitive to Fock representation in this deparametrized second-order adiabatic calculation.
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Prism Effect in Quantum Gravity
Extended Born-Oppenheimer coupling of the EM field to quantum geometry yields chromatic dispersion of light—a prism effect proposed as an all-energy quantum-gravity probe on a quantum FLRW background.
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Effective spherical symmetry in Loop Quantum Gravity: A path integral approach
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Effective Improved-GUP Cosmology: Emergent FLRW Universe without a Bounce
Improved GUP deformations applied to FLRW cosmology with Ashtekar-Barbero variables produce a non-singular emergent universe coasting from constant volume without a bounce and with a universal maximum energy density.
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Quantum Cosmology in Krylov Space: Complexity and Entropy
In a sharply peaked Gaussian state of a flat FLRW universe with a massless scalar clock, Krylov state complexity grows as σ²(φ−φ0)²/4 and operator complexity is exactly twice that, in both Wheeler-DeWitt and loop quan...
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Spinfoams, $\gamma$-duality and parity violation in primordial gravitational waves
γ-duality in the EPRL spinfoam model determines the relation between parity-even and parity-odd terms in an effective gravity theory, allowing the Barbero-Immirzi parameter to be measured from inflationary tensor observables.
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Quantum Cosmological Backreactions II: Purely Homogeneous Quantum Cosmology
Space adiabatic perturbation theory applied to homogeneous oscillator models shows that backreactions add correction terms to effective Hamiltonians neglected in the Born-Oppenheimer approximation.
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Polymer quantum mechanics on compact configuration spaces
Polymer quantization on compact spaces yields finite graph Hilbert spaces whose exact ring and box spectra recover Schrödinger QM as lattice spacing vanishes.
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Relational quantization of the Schwarzschild black hole interior resolves the singularity with a quantum bounce, finite Kretschmann scalar, bounded area, and black-hole-to-white-hole transition.
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The work calculates scalar quasinormal mode spectra for a rotating quantum-corrected black hole and constructs a methodological pipeline to infer the quantum correction parameter from gravitational-wave ringdown data ...
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Image of a quantum-corrected black hole without Cauchy horizons illuminated by a static thin accretion disk
For the no-Cauchy-horizon quantum-corrected metric, a larger quantum parameter produces larger horizon, photon sphere, ISCO, and shadow, with narrower and tighter-spaced photon and lensed rings.
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An Extended Second Law of Thermodynamics
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