Evidence for a very large scale fractal structure in the universe from COBE measurements

In this work, we analyse the temperature fluctuations of the cosmic microwave background radiation observed by COBE and show that the distribution can be fitted by a fractal distribution with a fractal dimension $ D= 1.43 pm 0.07 $. This value is in close agreement with the fractal dimension obtained by Coleman and Pietronero (1992) and Luo and Schramm (1992) from galaxy-galaxy and cluster-cluster correlations up to $ sim 100 h^{-1} Mpc$. The fact that the observed temperature fluctuations correspond to scales much larger than $ 100 h^{-1} Mpc$ and are signatures of the primordial density fluctuations at the recombination layer suggests that the structure of the matter at the early universe was already fractal and thus non-homogeneous on those scales. This result may have important consequences for the theoretical framework that describes the universe.