Modern astronomical instruments produce enormous amounts of three-dimensional data describing the physical Universe. The currently available data sets range from the solar system to nearby stars and portions of the Milky Way Galaxy, including the interstellar medium and some extrasolar planets, and extend out to include galaxies billions of light years away. Because of its gigantic scale and the fact that it is dominated by empty space, modeling and rendering the Universe is very different from modeling and rendering ordinary three-dimensional virtual worlds at human scales. Our purpose is to introduce a comprehensive approach to an architecture solving this visualization problem that encompasses the entire Universe while seeking to be as scale-neutral as possible. One key element is the representation of model-rendering procedures using power scaled coordinates (PSC), along with various PSC-based techniques that we have devised to generalize and optimize the conventional graphics framework to the scale domains of astronomical visualization. Employing this architecture, we have developed an assortment of scale-independent modeling and rendering methods for a large variety of astronomical models, and have demonstrated scale-insensitive interactive visualizations of the physical Universe covering scales ranging from human scale to the Earth, to the solar system, to the Milky Way Galaxy, and to the entire observable Universe.