Casting Loop Quantum Cosmology in the Spin Foam Paradigm

Abstract

The goal of spin foam models is to provide a viable path integral formulation of quantum gravity. Because of background independence, their underlying framework has certain novel features that are not shared by path integral formulations of familiar field theories in Minkowski space. As a simple viability test, these features were recently examined through the lens of loop quantum cosmology (LQC). Results of that analysis, reported in a brief communication [1], turned out to provide concrete arguments in support of the spin foam paradigm. We now present detailed proofs of those results. Since the quantum theory of LQC models is well understood, this analysis also serves to shed new light on some long standing issues in the spin foam and group field theory literature. In particular, it suggests an intriguing possibility for addressing the question of why the cosmological constant is positive and small.

37 pages, no figures. 3 references and half a dozen clarifications added. All changes are minor.

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Cited by in corpus (64)

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• Loop quantum gravity: the first twenty five years
• Perfect discretization of reparametrization invariant path integrals
• Lost in Translation: Topological Singularities in Group Field Theory
• Path Integrals and the WKB approximation in Loop Quantum Cosmology
• Cosmological constant in spinfoam cosmology
• A new look at loop quantum gravity
• Towards classical geometrodynamics from Group Field Theory hydrodynamics
• Group field cosmology: a cosmological field theory of quantum geometry
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• Loop Quantum Gravity
• Linking covariant and canonical LQG II: Spin foam projector
• Classical Setting and Effective Dynamics for Spinfoam Cosmology
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• Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity
• Path integral polymer propagator of relativistic and non-relativistic particles
• Comment on `Lost in Translation: Topological Singularities in Group Field Theory'
• Quantum Reference Frames at the Boundary of Spacetime
• Reduced Phase Space Quantization of Black Holes: Path Integrals, and Effective Dynamics
• Vertex Expansion for the Bianchi I model
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• Coherent State Functional Integral in Loop Quantum Cosmology: Alternative Dynamics
• Path Integrals and Alternative Effective Dynamics in Loop Quantum Cosmology
• Higher dimensional Loop Quantum Cosmology
• Two-point functions in (loop) quantum cosmology
• Unimodular Loop Quantum Cosmology
• Loop Quantum Cosmology
• Coherent states for FLRW space-times in loop quantum gravity
• The Lorentzian proper vertex amplitude: Classical analysis and quantum derivation
• Coherent State Functional Integrals in Quantum Cosmology
• Spin-foam model for gravity coupled to massless scalar field
• Diffeomorphism invariant cosmological sector in loop quantum gravity
• The consistent histories approach to loop quantum cosmology
• Spinfoams: Foundations
• Dynamical eigenfunctions and critical density in loop quantum cosmology
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• Gravitational waves with generalized holonomy corrections
• Toward matter dynamics in spin foam quantum gravity
• Loop quantum cosmology in 2+1 dimension
• Relativistic Planck-scale polymer
• Solvable Loop Quantum Cosmology: domain of the volume observable and semiclassical states
• Loop quantum cosmological dynamics of scalar-tensor theory in the Jordan frame
• Causal structure in spin-foams
• Local spin foams
• Alternative $k=-1$ loop quantum cosmology
• Path Integral of Bianchi I models in Loop Quantum Cosmology
• The Physical Relevance of the Fiducial Cell in Loop Quantum Cosmology
• A note on the scalar products in sLQC
• Quantum Big-Bounce as a phenomenology of RQM in the Mini-superspace
• Cosmological dynamics in spin-foam loop quantum cosmology: challenges and prospects
• On the Role of Fiducial Structures in Minisuperspace Reduction and Quantum Fluctuations in LQC
• Cosmic tango between the very small and the very large: Addressing CMB anomalies through Loop Quantum Cosmology