Robustness of key features of loop quantum cosmology

By Abhay Ashtekar, Alejandro Corichi, Parampreet Singh. 2007

411 citations recorded by the source corpus.

A small simplification based on well-motivated approximations is shown to make loop quantum cosmology of the $k=0$ Friedman-Robertson-Walker model (with a massless scalar field) exactly soluble. Analytical methods are then used i) to show that the quantum bounce is generic; ii) to establish that the matter density has an absolute upper bound which, furthermore, equals the critical density that first emerged in numerical simulations and effective equations; iii) to bring out the precise sense in which the Wheeler-DeWitt theory approximates loop quantum cosmology and the sense in which this approximation fails; and iv) to show that discreteness underlying loop quantum cosmology is fundamental. Finally, the model is compared to analogous discussions in the literature and it is pointed out that some of their expectations do not survive a more careful examination. An effort has been made to make the underlying structure transparent also to those who are not familiar with details of loop quantum gravity.

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

View Paper: https://www.semanticscholar.org/paper/8f476f9836a77d5d8515fa4b389dd808b875e75f

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Citations in the corpus

Loop Quantum Gravity (2003, neutral): “See [129] and references therein.”
Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates (2016, methodology): “Using the non-perturbative quantization techniques of LQG, in LQC it has been possible to obtain a well-defined quantum theory for FLRW space–times where the big-bang and bigcrunch singularities are resolved [29, 30, 95].”
Introduction to Loop Quantum Cosmology (2011, methodology): “41 times the Planck density) on the whole physical Hilbert space [12].”
Loop quantization of the Schwarzschild interior revisited (2015, background): “5 In the LQC literature β is sometimes taken as β = 4 √ 3πγ, but one can also see it as a free parameter to be determined by physical considerations [4].”
Inflationary Cosmology in Modified Gravity Theories (2015, methodology): “Particularly, we consider inflation (i) derived by modification terms of gravity [26]; (ii) through the quantum anomaly [27]; and (iii) in R gravity in the framework of the so-called loop quantum cosmology (LQC) [29–33] to include quantum effects [28] (for reviews on LQC, see, for example, [34–40]).”
From black holes to white holes: a quantum gravitational, symmetric bounce (2017, neutral): “Preservation of this condition upon evolution 0 ≈ ˙̃Ψ = {P1, HLQC} − 1, (B1) 21 and after evaluation on shell, allows us to fix the lapse function N = c b γ2 8π √ δc 2 |O2| cosh (4GγP2) 1 δb √ 1− b2o tanh2 [ GγboT̃ ] .”