Abstract
The Weyl curvature constitutes the radiative sector of the Riemann curvature tensor and gives a measure of the anisotropy and inhomogeneities of spacetime. Penrose’s 1979 Weyl curvature hypothesis (WCH) assumes that the universe began at a very low gravitational entropy state, corresponding to zero Weyl curvature, namely, the Friedmann–Lemaître–Robertson–Walker (FLRW) universe. This is a simple assumption with far-reaching implications. In classical general relativity, Belinsky, Khalatnikov and Lifshitz (BKL) showed in the 70s that the most general cosmological solutions of the Einstein equation are that of the inhomogeneous Kasner types, with intermittent alteration of the one direction of contraction (in the cosmological expansion phase), according to the mixmaster dynamics of Misner (M). How could WCH and BKL-M co-exist? An answer was provided in the 80s with the consideration of quantum field processes such as vacuum particle creation, which was copious at the Planck time (10−43 s), and their backreaction effects were shown to be so powerful as to rapidly damp away the irregularities in the geometry. It was proposed that the vaccum viscosity due to particle creation can act as an efficient transducer of gravitational entropy (large for BKL-M) to matter entropy, keeping the universe at that very early time in a state commensurate with the WCH. In this essay I expand the scope of that inquiry to a broader range, asking how the WCH would fare with various cosmological theories, from classical to semiclassical to quantum, focusing on their predictions near the cosmological singularities (past and future) or avoidance thereof, allowing the Universe to encounter different scenarios, such as undergoing a phase transition or a bounce. WCH is of special importance to cyclic cosmologies, because any slight irregularity toward the end of one cycle will generate greater anisotropy and inhomogeneities in the next cycle. We point out that regardless of what other processes may be present near the beginning and the end states of the universe, the backreaction effects of quantum field processes probably serve as the best guarantor of WCH because these vacuum processes are ubiquitous, powerful and efficient in dissipating the irregularities to effectively nudge the Universe to a near-zero Weyl curvature condition.
Highlights
The Weyl curvature constitutes the radiative sector of the Riemann curvature tensor and gives a measure of the anisotropy and inhomogeneities of spacetime
We point out that regardless of what other processes may be present near the beginning and the end states of the universe, the backreaction effects of quantum field processes probably serve as the best guarantor of Weyl curvature hypothesis (WCH) because these vacuum processes are ubiquitous, powerful and efficient in dissipating the irregularities to effectively nudge the Universe to a near-zero Weyl curvature condition
Before we begin our studies of WCH in a quantum setting it is important to remind ourselves of the two very important theoretical achievements in the 60s in classical general relativity (GR), which underlie all investigations in black holes and cosmology built upon the GR theoretical framework: the singularity theorems from 1965–1968 of Penrose [44], Hawking [45] and Geroch [46], and the general solutions of the Einstein equations near the cosmological singularity in the work of Belinsky, Khalatnikov, Lifshitz (BLK) from the early 60s to the early 1970s [47–49] with the famous
Summary
Penrose pointed out in his 1979 essay [3] that if our Universe had begun close to what the Friedmann–Lemaître–Robertson–Walker (FLRW) models describe, in a state of highest degree of isotropy and homogeneity, corresponding to zero Weyl curvature, it is something extremely special He reached this conclusion by comparing the entropy of matter we see today, measured by the Hawking radiation, emitted by black holes, to the entropy of gravity, measured by the Weyl curvature tensor squared integrated over. Most people would agree that quantum effects are important at the beginning and ending stages of the universe, either entering a singularity or with a minimal scale These developments and considerations add new impetus and interests to Penrose’s WCH-GEnt, originally formulated without quantum considerations. The latter pertains to LQC: It concerns the effects of the inhomogeneous quantum modes in the superspace of 3-geometries, so far largely ignored in the minisuperspace formulations of LQC
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