Comparison of loop quantum cosmology and Wheeler-DeWitt quantum cosmology

Abstract: Quantum geometrodynamics and loop quantum gravity are two canonical approaches to quantum gravity. Their corresponding cosmological theories, Wheeler-DeWitt quantum cosmology and loop quantum cosmology, give different results for the same cosmological model. We use a flat isotropic homogeneous universe coupled to a massless scalar field and calculate in both theories the quantized Hamiltonian constraint, the wave packets, the Hubble parameter, and the volume expectation value. We see that both the Hubble parameter and the volume expectation values show different behavior in LQC and WDW theory. We also look at the criticism about certain assumptions in LQC and comment on the singularity avoidance claims in LQC. To understand the criticism well, we calculate the quantum fluctuations of the volume operator.

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Using reference fluids for quantum gravity corrections to quantum field theory

Abstract: Due to gravity being a constrained theory, the Universe evolution is plagued by a 'freezing' in the canonical quantum formalism, as the implementation of the Dirac scheme dictates no evolution in time. A possible solution is to define a time parameter from existing variables to regain standard QFT evolution, and one can even go to the next order with a perturbative expansion, to infer the quantum gravitational corrections to the quantum matter dynamics. We illustrate an implementation of the reference frame fixing procedure, as in the Kuchar-Torre proposal, using the Gaussian frame (that materializes as a fluid in the theory) to construct a suitable time. The gravity-matter system is also separated in a Born-Oppenheimer-like way: the slow varying component, that is gravity, obeys the Wheeler-DeWitt equation, while the fast quantum sector is composed of the matter plus the Gaussian fluid. With a perturbative expansion in a Planckian parameter, the dynamics for the matter sector is inferred, finding a Hermitian Hamiltonian with the Gaussian fluid as a physical clock. We show that this outcome is equivalent to the result with the kinematical action, first introduced by Kuchar, in the homogeneous setting. We also present an application to a cosmological toy model, mimicking the slow-roll phase.

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A new pathway to the no-boundary proposal using complex allowable metrics

Abstract: In this talk I will explain how the concept of allowable complex metrics recently defined by Kontsevich and Segal may open a new pathway towards an understanding of the early quantum state of the universe, as first described forty years ago by the no-boundary proposal of Hartle and Hawking. This proposal builds a wavefunction of the early universe and provides one of the rare theories of initial conditions for our universe. The wavefunction was originally thought of as a path integral summing over all compact and regular Euclidean metrics. Many discussions on the precise mathematical implementation of this definition followed, and so far no unanimously accepted picture has been reached. A few months ago, the concept of allowable complex metrics as those on which quantum field theories can be defined consistently was introduced by Kontsevich and Segal. Applying this to gravity, Witten found that allowable complex metrics are typically giving physically meaningful results, while non-allowable ones lead to nonsensical results. Here I will focus on the application of this concept to no-boundary examples in a minisuperspace model, both for isotropic and anisotropic cases. I will discuss how this can provide new insights on long lasting puzzles of the no boundary proposal, such as guidance about which lapse contour integral must be chosen, or justification for why scalar fields should start on a location favoring the beginning of an inflationary phase.

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Canonical Formulation of the Oppenheimer-Snyder Model for Gravitational Collapse

Abstract: The Oppenheimer-Snyder (OS) model is a simple model for gravitational collapse. We hope that its quantisation might prove as an interesting area of research, which could lead to a deeper understanding of quantum gravity. In order to lay the groundwork, we cast the OS model into canonical form for all possible curvatures of the Friedmann interior at once. This is done by removing excess terms in the action by finding appropriate expressions for the Schwarzschild time on the dust cloud’s surface. One particular time coordinate for each case will emerge naturally: Painlevé-Gullstrand (PG), generalised Painlevé-Gullstrand (GPG) and Gautreau-Hoffmann (GH) coordinates for the flat, open and closed cases, respectively.

Two observers are of interest: a comoving observer and a stationary observer. The former sits at the dust cloud’s surface and moves alongside it. The latter takes the role of someone stationed far away who observes the collapse. Each of them present us a unique scenario of the collapse. The comoving observer allows us to see past the event horizon, whereas the stationary observer is interesting from an astrophysical standpoint. We on Earth are stationary observers which observe gravitational collapses from far away. The change between the comoving and stationary observer is implemented by turning the coordinate transformation between the comoving observer’s proper time and the Schwarzschild time into a canonical transformation.

Furthermore, we present two Hamiltonian constraints, one for each observer, which we deparametrise to obtain the physical Hamiltonians for the observers. A consistency check between the equations of motion obtained from the new Hamiltonians and the equations of motion obtained from a general discussion of the OS model serves as a verification for the validity of these new Hamiltonians.

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