AUTHOR=Sonoda Tomohide 

TITLE=Self-Similar Symmetry Model and Cosmic Microwave Background

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=Volume 2 - 2016

YEAR=2016

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2016.00005

DOI=10.3389/fams.2016.00005

ISSN=2297-4687

ABSTRACT=In this paper, we present the self-similar symmetry (SSS) model that describes the hierarchical structure of the universe. The model is based on the concept of self-similarity, which explains the symmetry of the cosmic microwave background (CMB). The approximate length and time scales of the six hierarchies of the universe---grand unification, electroweak unification, the atom, the pulsar, the solar system, and the galactic system---are derived from the SSS model. In addition, the model implies that the electron mass and gravitational constant could vary with the CMB radiation temperature.