Local Scale Covariance and Its Radical Implications for Cosmology

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.