Abstract
Local scale covariance posits that no privileged length scales should appear in the fundamental equations of local, Minkowskian physics—why should nature have scale, but not position preferences?—yet, they clearly do. A resolution is proposed wherein scale covariance is promoted to the status of Poincaré covariance, and privileged scales emerge as a result of ‘scale clustering’, similarly to the way privileged positions emerge in a translation covariant theory. The implied ability of particles to ‘move in scale’ has recently been shown by the author to offer a possible elegant solution to the missing matter problem. For cosmology, the implications are: (a) a novel component of the cosmological redshift, due to scale-motion over cosmological times; (b) a radically different scenario for the early universe, during which the conditions for such scale clustering are absent. The former is quantitatively analyzed, resulting in a unique cosmological model, empirically coinciding with standard Einstein–de-Sitter cosmology, only in some non-physical limit. The latter implication is qualitatively discussed as part of a critique of the conceptual foundations of ΛCDM which ignores scale covariance altogether.
Highlights
For over a millennium, astronomers agreed on an observationally sound cosmological model which was founded on the premise that humans are at the center of the universe
The reason why most physicists do not consider the lack of scale covariance a problem is, probably, that nature does appear to single out privileged scales
Why challenge the concordance model? Despite being experimentally rather sound, ΛCDM rests on shaky conceptual foundations
Summary
Astronomers agreed on an observationally sound cosmological model which was founded on the premise that humans are at the center of the universe They have since become much more modest with the inclusion of translation covariance as a fundamental principle in physics, but without treating scale covariance on equal footing, the primitive sin of anthropocentrism will not be fully atoned. Scale covariance is just as natural a symmetry as translation covariance: a fundamental description of nature should not include a privileged length scale, just like it should not include a privileged position; Both ought to appear as attributes of specific solutions rather than of the equations Is just another constraint imposed on a representation of matter for the reasons given above
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