Constant Acceleration in Fractal Structures with Fractal Dimension D = 2

Abstract

An unexplained acceleration on the order of 10–8 cm s–2, which is close to cH, where c is the speed of light and H is the Hubble constant, is detected in gravitationally bound systems of different scales, from the solar system to clusters of galaxies. We found that any test body located inside a fractal structure with fractal dimension D = 2 experiences acceleration of the same order and confirmed the previous work that photons propagating through this structure decrease the frequency owing to gravitational redshift. The acceleration can be directed against the movement of the test body. The fractal distribution of the matter should be at scales of at least hundreds of megaparsecs to a few gigaparsecs for the existence of this acceleration.