It appears as one of the fundamental principles of Nature that the equations expressing basic laws should be invariant under the widest possible group of transformations. ~ English theoretical physicist Paul Dirac
Quantum physics explains the emergence of matter from coherent, localized energy fields, emanating out of a ground state (vacuum) which itself seethes with tremendous energy. Quantization of energy is the fundamental mechanism by which existence manifests. Therefore, materiality must have a spatial metric in its origination.
Vacuum at the quantum level is not scale-invariant, since some units of mass, length and time can be defined on the basis of the Planck constant. However, large-scale empty space differs by an enormous factor (1039) from the quantum scales. Empty space at large scales could have scale invariance, since by definition there is nothing to define a scale. ~ André Maeder
Actuality emerges at the quantum scale, with physics which are unique to the subatomic realm. There is no reason to think that empty ambient space is dependent upon scale, certainly not like quantum mechanics are in relation to the ground state. In other words, there appears to be a fundamental discontinuity between quantum quantization and the ambient world, which is ruled by electrodynamics. At the stellar scale, gravity becomes more pronounced in its effects.
Galileo discovered that the laws of physics have no scale (Galilean invariance). Einstein’s general relativity theory revealed matter warping the very spacetime fabric that defines existence. The relation between mass and gravity were considered constant, thereby scale-invariant.
The equations which describe electrodynamics, in absence of charges and currents, are scale-invariant; so too cosmic interplay via gravity.
Empty space at large scales is scale-invariant. ~ André Maeder
A cosmological model assuming scale invariance corresponds with all astronomical observations, and all macroscopic physics theories. Dark matter and dark energy disappear with a scale-invariant cosmological model: Nature goes about its business without need to invoke a mystical glue to hold the universe together, or phantom energy to nudge comportment with actuality.