Fractal turbulence and the origin of the galaxies and of the large-scale structure

Observations show that the geometry of the large-scale distribution of galaxies is like a self-similar sponge which can be regarded as a fractal in fractal geometry (the Sierpinski sponge) with the fractal dimensionD _f=3–, =1.7–1.8 is the index in the two-point correlation function.We suggest using a new scheme to explain the origin of galaxies and large-scale structure. In our model, we assume that the density perturbations in the early Universe are adiabatic, and once they come within the horizon, they might produce the vortices of the fractal turbulence because of the Thomson drag. A model of the fractal turbulence is also given in this paper. The results obtained show that the basic characteristics of the galaxies (massM _g, angular momentumJ _g) and the large-scale structure (fractal dimensionD _f) can be explained, if the spectrum of early perturbations is the scale-free Zeldovich spectrum.