Information Theory of Evolutionary Stages in Noninteger Dimensional Spaces

This paper investigates evolution of a physical system through intermediate noninteger dimensions to provide a phenomenological explanation for the system’s emergent properties. In recent papers it was shown that physical space is associated with noninteger dimensionality and its value is associated with the strength of attractive inverse square law and this has applications to diverse fields including the design of metamaterials. Here this information-theoretic analysis is applied to cosmology to yields a novel noninteger dimensional explanation for filaments and sheets of matter, inflation, and the accelerating expansion of the universe, without the need to postulate inflation field or dark energy as the drivers of this expansion. Furthermore, the analysis shown that in the future as the zero-dimension residual potential declines further, the expansion will slow and then reverse. Evolution across noninteger spaces has potential relevance for the study of materials that emerge from compressing three-dimensional volumes into lower dimensions.