If we take Planck's constant to be a measure of quantum fluctuations, which seems natural in the world-view of this topic (which discusses "random fields"), then it also seems natural to ask whether Planck's constant might vary over cosmological scales, just as temperature is a measure of thermal fluctuations and varies over cosmological scales. I had better note here that the difference between quantum fluctuations and thermal fluctuations, in a random field world-view, is a fundamental one of symmetry properties: quantum fluctuations are invariant under the Poincaré group, while thermal fluctuations are invariant only under a little group (of the Poincaré group) that leaves a time-like vector invariant. A moderately detailed account is given in the above topic and in the various published papers it cites. I'm not competent to enter detailed discussions on cosmology, but hopefully my question will be answerable: "Are there cosmological models in which Planck's constant varies?" One justification for taking thermal fluctuations to be strongly related to quantum fluctuations in principle is the Unruh effect, under which the quantum vacuum appears thermal to an accelerating observer. Similarly, under the Hawking effect, variations of the metric have thermal properties, as one would expect from the principal of equivalence. General covariance would appear to require a unified description of thermal and quantum fluctuations. Since a variation of quantum fluctuations would presumably have effects comparable to those of variations of thermal fluctuations -- in an approximate description it would exert a force -- it seems possible that one reconceptualization of metric variation might be as variation of quantum fluctuations. There is a supplementary point that I would also like to make. If we ever talk about "quantum fluctuations", which Physicists often do without offering any details of what quantum fluctuations might be, then there arises the question of quantum entropy as the thermodynamic dual of Planck's constant, just as thermal entropy is the thermodynamic dual of temperature. Note that entropy is not a Lorentz invariant concept, its definition requires a phase space to be introduced. The existence of quantum fluctuations, if taken seriously, has serious consequences for arguments that fundamentally rely on entropy.