  Penrose's 1979 Weyl curvature hypothesis (WCH) \cite{WCH} assumes that the
universe began at a very low gravitational entropy state, corresponding to zero
Weyl curvature, namely, the FLRW universe. This is a simple assumption with
far-reaching implications. In classical general relativity the most general
cosmological solutions of the Einstein equation are that of the BKL-Misner
inhomogeneous mixmaster types. 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 ($10^{-43}
sec$), 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
vacuum 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. 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.
