Conceptual Problems in Quantum Gravity and Quantum Cosmology

Abstract

The search for a consistent and empirically established quantum theory of gravity is among the biggest open problems of fundamental physics. The obstacles are of formal and of conceptual nature. Here, I address the main conceptual problems, discuss their present status and outline further directions of research. For this purpose, the main current approaches to quantum gravity are briefly reviewed and compared.

41 pages, invited review

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Cited by in corpus (55)

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• Quantum signatures of black hole mass superpositions
• Swampland conjecture in $f(R)$ gravity by the Noether Symmetry Approach
• Optomechanical tests of a Schrödinger-Newton equation for gravitational quantum mechanics
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• Study of the Inflationary Spectrum in the Presence of Quantum Gravity Corrections
• Non-commutative black holes of various genera in the connection formalism
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• Classical and quantum bicosmology with noncommutativity
• Dirac observables and boundary proposals in quantum cosmology
• Quantum cosmological intertwining: Factor ordering and boundary conditions from hidden symmetries
• Quantum cosmological consistency condition for inflation
• Third quantization for scalar and spinor wave functions of the Universe in an extended minisuperspace
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• Emergent dark energy via decoherence in quantum interactions
• Spinorial Wheeler-DeWitt wave functions inside black hole horizons
• Cosmological production of black holes: a way to constrain alternative theories of gravity
• "Time"-covariant Schrödinger equation and the canonical quantization of the Reissner-Nordström black hole
• Einstein-Cartan-Dirac equations in the Newman-Penrose formalism
• Entanglement entropy at critical points of classical evolution in oscillatory and exotic singularity multiverse models
• Quantum-Ordering Ambiguities in Weak Chern-Simons 4D Gravity and Metastability of the Condensate-Induced Inflation
• Primordial Universe with radiation and Bose-Einstein condensate
• Quantum Gravity from the Composition of Spacetime Constructed through Generalised Proper Time
• Hawking radiation and black hole gravitational back reaction - A quantum geometrodynamical simplified model
• Evidence of time evolution in quantum gravity
• Classical and quantum cosmology of Fab Four John theories
• Classical geodesics from the canonical quantisation of spacetime coordinates
• Impact of trans-Planckian quantum noise on the Primordial Gravitational Wave spectrum
• Some exact results on quantum Newtonian cosmology
• Unitary and non-unitary transitions around a cosmological bounce
• A New Guest in the Third Quantized Multiverse
• Bouncing and Cyclic Quantum Primordial Universes and the Ordering Problem
• Quantum Entanglement Dynamics of Spacetime and Matter
• The rotation problem
• Potential of Neutrino Telescopes to Detect Quantum Gravity-Induced Decoherence in the Presence of Dark Fermions
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• Mimetic Horava Gravity and Surface terms
• Quantum Reference Frames via Transition Amplitudes in Timeless Quantum Gravity
• Lorentz Gauge Theory of Gravity in Electron Positron Colliders
• Ideal Quantum Gases with Planck Scale Limitations
• Universal Entanglement and an Information-Complete Quantum Theory
• Space, Time, Matter in Quantum Gravity
• Wheeler-DeWitt Universe Wave Function in the presence of stiff matter
• Constructibility of the universal wave function
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• Towards an Alternative Gravitational Theory
• Concerning Infeasibility of the Wave Functions of the Universe
• Time-covariant Schrödinger equation and invariant decay probability: The $\Lambda$-Kantowski-Sachs universe
• Is spacetime quantum?
• Towards a unified Lagrangian formalism for Cosmology and Black Holes
• Fermionic quantum cosmology as a framework for resolving type IV singularities
• An approximate application of quantum gravity to the rotation problem