The Application of Dimensional Analysis to Cosmology or - how to Make Cosmology Simple by Using Dimensional Conspiracy
Cosmology as it is usually studied suffers from the problem that no criterion is known which isolates from the large class of models allowed by the equations of physics those few which are realized in Nature. To provide such a criterion, it is proposed that cosmology should be based on the study of models which are free of arbitrary scales or units, this condition being compatible with (but not identical with) the Cosmological Principle. Formally, the basis for scale-free cosmology can be expressed in a dimensional Conspiracy Hypothesis: The material parameters of a system (mass, density, pressure etc.), the constants of physics and the coordinates have realizable physical meanings only when they occur together in dimensionless combinations (η-numbers) in which the components may vary with time or place but in such a manner that the variations conspire to keep the η-numbers constant. The Conspiracy Hypothesis (CH) streamlines cosmology, simplifying it to the finding of a few dimensionless numbers. Applied to Einstein's general relativity, the CH yields a simple cosmological model consisting of static clusters of galaxies with inverse-square density profiles embedded in an expanding, homogeneous background. This model agrees well with the observed Universe insofar as the latter can be described by general relativity. The CH can also be applied to other theories of gravity, especially those in which the gravitational parameter G is variable, and can also in itself be taken as a basis for gravitational theory.