Weyl Curvature Hypothesis in Light of Quantum Backreaction at Cosmological Singularities or Bounces
Abstract
:Preface
1. Weyl Curvature Hypothesis and Gravitational Entropy
1.1. Classical GR
1.1.1. Singularity Theorems: Penrose-Hawking-Ellis-Geroch
1.1.2. Approach to Cosmological Singularity: BKL-Misner
1.1.3. Weyl Curvature
1.1.4. Gravitational Entropy: Weyl and Other Measures
1.2. Semiclassical Gravity: Entropy of Gravitons and WCH
1.2.1. Graviton Backreaction in FLRW Universes
1.2.2. Entropy of Gravitons in the Gowdy Universe
2. Cyclic Cosmology and Trace-Anomaly Induced Bounces
2.1. Penrose’s Conformal Cyclic Cosmology (CCC)
2.2. Cyclic Cosmology from Particle/ String Models. Big Crunch
2.2.1. Cyclic and Ekpyrotic Cosmologies
2.2.2. Big Crunch with Dark Energy in Semiclassical Cosmology
2.3. Semiclassical Gravity: Trace Anomaly Induced Bounces
3. Singularity Avoidance in Quantum Cosmology
3.1. Quantum Cosmology: Bounce in Gowdy Universe
3.2. Quantum BKL-Mixmaster Scenarios
3.3. Loop Quantum Cosmology (LQC): ‘Big Bounce’?
4. Quantum Phase Transition and Quantum Backreaction
4.1. Quantum Phase Transition: Continuum to Discrete
4.2. Quantum Backreaction of Inhomogeneous Superspace Modes
5. Semiclassical Backreaction Supports WCH
5.1. Damping of Irregularities Ensures a Smooth Transition, Critical for Cyclic Cosmologies
5.2. Quantum Gravity: Macro Spacetime Manifold from the Interaction of Micro Constituents
5.3. Quantum Cosmology: Singularity or Bounce Ruled by the Interaction of Micro-Constituents
Funding
Acknowledgments
Conflicts of Interest
1 | This list is far from exhaustive. We are not treating inflationary cosmology [31,32,33,34] here, since it already has a wide coverage and how the WCH fits in with inflation is rarely discussed. On the relation of inflation and singularity, Borde and Vilenkin [35] made a categorical statement that a physically reasonable spacetime that is eternally inflating to the future must possess an initial singularity. Vilenkin [36] also questioned the necessity of quantum cosmology in the face of eternal inflation. As for the speculations into our universe’s future, there is considerable amount of work based on two types of inflationary models, one is the ‘stochastic inflation’ of Starobinsky [37,38] which allows the noise associated with the fluctuations of a quantum field to drive the universe to inflation. The other is the ‘eternal inflation’ proposed and developed by Linde, Vilenkin, Guth and others [39,40], where a universe can live forever with the continual births of baby universes in the sequential and parallel generation of multiple branches. For a recent assessment of the likelihood for eternal inflation in a variety of popular models, including the swampland of string theory, see, e.g., [41,42,43]. |
2 | |
3 | An important exception is the case when a massless scalar field is present, which obeys an equation of state like a stiff fluid, and, in Friedmann models, has the same dependence of the density on the scale factor as anisotropies (). As is rigorously shown in [71], such a scalar field will suppress the BKL oscillations during the evolution towards the singularity. The relevance of stiff matter in the early universe is noted by Barrow [72]. |
4 | This diagonal form has full generality because there is no spatial curvature. In a Bianchi Type IX universe where the spatial curvature is present, spacetimes represented by the full matrix are more general than that of the diagonal metric which is Misner’s mixmaster universe [50]; the off-diagonal components signify rotation [74]. |
5 | An element of craziness needs to creep in before an idea ascends to the order of the three Fs: Fashion, Faith, and Fantasy. I read this as a warning of an enlightened guru speaking to his present adherents and future believers: Safeguard your independent thinking before you become completely converted. |
6 |
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Hu, B.-L. Weyl Curvature Hypothesis in Light of Quantum Backreaction at Cosmological Singularities or Bounces. Universe 2021, 7, 424. https://doi.org/10.3390/universe7110424
Hu B-L. Weyl Curvature Hypothesis in Light of Quantum Backreaction at Cosmological Singularities or Bounces. Universe. 2021; 7(11):424. https://doi.org/10.3390/universe7110424
Chicago/Turabian StyleHu, Bei-Lok. 2021. "Weyl Curvature Hypothesis in Light of Quantum Backreaction at Cosmological Singularities or Bounces" Universe 7, no. 11: 424. https://doi.org/10.3390/universe7110424
APA StyleHu, B. -L. (2021). Weyl Curvature Hypothesis in Light of Quantum Backreaction at Cosmological Singularities or Bounces. Universe, 7(11), 424. https://doi.org/10.3390/universe7110424