Exploration of the density–size correlation of celestial objects on various scales

In the 1930s, Edwin Francis Carpenter calculated a size density restriction and correlation for galaxy clusters. This was reworked by Gerard de Vaucouleurs in the 1970s, proving an improved and expanded size density correlation. However, these papers still use legacy datasets, some of which do not contain data of high precision and accuracy collected by modern observational tools. To address this limitation, we used modern datasets to reinvestigate and redefine the correlation between the density and size of celestial objects in the universe. Specifically, we sought to analyze the density and size data of various celestial objects, such as neutron stars, galaxies, and galaxy clusters, and determine if a linear relationship exists between their densities and sizes. We hypothesized a negative linear correlation exists on all celestial object scales. Through logarithmically graphing data, we found that this negative correlation of luminous matter exists on such scales. We postulate that this negative correlation implies a hierarchical view of the universe, and the repeating pattern on multiple scales suggests a fractal cosmology of the universe.