Symmetries of the Large Scale Structures of the Universe as a Phenomenology of a Fractal Turbulence: The Role of the Plasma Component

We present a new perspective on the symmetries that govern the formation of large-scale structures across the Universe, particularly focusing on the transition from the seeds of galaxy clusters to the seeds of galaxies themselves. We address two main features of cosmological fluid dynamics pertaining to both the linear and non-linear regimes. The linear dynamics of cosmological perturbations within the Hubble horizon is characterized by the Jeans length, which separates stable configurations from unstable fluctuations due to the gravitational effect on sufficiently large (and therefore, massive enough) overdensities. On the other hand, the non-linear dynamics of the cosmological fluid is associated with a turbulent behavior once the Reynolds numbers reach a sufficiently high level. This turbulent regime leads to energy dissipation across smaller and smaller scales, resulting in a fractal distribution of eddies throughout physical space. The proposed scenario suggests that the spatial scale of eddy formation is associated with the Jeans length of various levels of fragmentation from an original large-scale structure. By focusing on the fragmentation of galaxy cluster seeds versus galaxy seeds, we arrived at a phenomenological law that links the ratio of the two structure densities to the number of galaxies in each cluster and to the Hausdorff number of the Universe matter distribution. Finally, we introduced a primordial magnetic field and studied its influence on the Jeans length dynamics. The resulting anisotropic behavior of the density contrast led us to infer that the main features of the turbulence could be reduced to a 2D Euler equation. Numerical simulations showed that the two lowest wavenumbers contained the major energy contribution of the spectrum.