Loop quantum cosmology of k = 1 FRW models

By Abhay Ashtekar, T. Pawłowski, Parampreet Singh, K. Vandersloot. 2006

332 citations recorded by the source corpus.

The closed, $k=1$, FRW model coupled to a massless scalar field is investigated in the framework of loop quantum cosmology using analytical and numerical methods. As in the $k=0$ case, the scalar field can be again used as emergent time to construct the physical Hilbert space and introduce Dirac observables. The resulting framework is then used to address a major challenge of quantum cosmology: resolving the big-bang singularity while retaining agreement with general relativity at large scales. It is shown that the framework fulfills this task. In particular, for states which are semiclassical at some late time, the big bang is replaced by a quantum bounce and a recollapse occurs at the value of the scale factor predicted by classical general relativity. Thus, the ``difficulties'' pointed out by Green and Unruh in the $k=1$ case do not arise in a more systematic treatment. As in $k=0$ models, quantum dynamics is deterministic across the deep Planck regime. However, because it also retains the classical recollapse, in contrast to the $k=0$ case one is now led to a cyclic model. Finally, we clarify some issues raised by Laguna's recent work addressed to computational physicists.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/28e8a146ff2dcb66deeaaec082dc20549a84f996

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Citations in the corpus

Planck stars (2014, background): “The bounce is due to a quantumgravitational repulsion which originates from the Heisenberg uncertainty, and is akin to the “force” that keeps an electron from falling into the nucleus [16].”
Loop quantum cosmology: a status report (2011, methodology): “μ̄ dynamics has been successfully implemented in the case of a non-zero cosmological constant [53, 55–57], the k=1, spatially compact case [58, 59], and to the Bianchi models [3, 60–62].”
On the semiclassical limit of 4d spin foam models (2008, background): “This problem has been explored by many authors and from various angles: for example, by the use of semiclassical states [1]–[6], by the extraction of propagators from spin foam models [7]–[9], by numerical simulations [10, 11] and by symmetry reduction [12]–[14].”
Quantum-gravity effects outside the horizon spark black to white hole tunneling (2014, background): “[17] A.”
Loop quantum cosmology of Bianchi I models (2009, methodology): “This scenario is borne out in the k=0, Λ=0 models, [6–13], Λ 6=0 models [14, 15], the k=1 closed model [16, 17], k=−1 open model [18] and the k=0 model with an inflationary potential with phenomenologically viable parameters [19].”
Introduction to Loop Quantum Cosmology (2011, background): “However, instead of a single-bounce event one now has a cyclic model [22].”
Extension of the quantum theory of cosmological perturbations to the Planck era (2012, background): “[16] A.”
New spinfoam vertex for quantum gravity (2007, background): “We hope that the developments presented here will contribute to the promising recent advances in understanding the low energy limit of LQG, such as the ones on the graviton propagator [3, 11, 12, 22], on the emergence of effective actions for matter [23], or on applications to cosmology [24] and bla”
Loop quantum cosmology: an overview (2008, methodology): “(For details, see [27].”
The pre-inflationary dynamics of loop quantum cosmology: confronting quantum gravity with observations (2012, methodology): “This behavior has been established analytically in the k = 0, = 0 case [60] and was checked numerically in the k = 1, as well as = 0 cases [27, 29, 31].”
Loop Quantum Cosmology (2005, background): “However, the situation is not fully clarified since the original versions, where the magnitudes of higher power and inverse volume corrections were compared numerically [26, 27, 28], were based on formulations of isotropic loop quantum cosmology, where inverse volume corrections are artificially sup”