![]() ![]() However, the magnitude of the final value of the scale of homogeneity shall not diminish the importance of the fractal structure on lower scales, namely, in the highly nonlinear clustering regime. In spite of the work of many cosmologists along several decades, e.g., Peebles, the debate about the scale of transition to homogeneity is not fully settled. In fact, fractal models of the universe predate the discovery of the cosmic web structure and arose from the idea of a hierarchy of galaxy clusters that continues indefinitely towards the largest scales, an idea championed by Mandelbrot. This motivates its study by means of fractal geometry. In fact, the range of sizes is so large that we can speak of a self-similar structure. The cosmic web is a foam-like structure, formed by a web of sheets surrounding voids of multiple sizes. The geometry and formation of this web structure are the subject of this study. This model generates the well-known cosmic web structure. Indeed, the successful adhesion model of large-scale structure formation is actually a model of turbulence in irrotational pressureless flow. The dissipation is essentially a transfer of kinetic energy from one scale to another smaller scale, due to nonlinear mode coupling, as is characteristic of fluid turbulence. This signals the end of a dust-like description of the matter dynamics and the need for a finer description of it, in which dissipative processes, in particular, play a prominent role. Then, large overdensities arise that decouple from the global expansion. These perturbations grow, and they grow faster on smaller scales, becoming nonlinear. ![]() #FRACTAL GEOMETRY PLUS#Although the Einstein equations of the theory of general relativity are nonlinear and difficult to solve, the early evolution of the universe can be described by an exact solution, namely, the FLRW solution, plus its linear perturbations. The evolution of the universe at large is ruled by gravity. The formation of the cosmic web is best modeled as a type of turbulent dynamics, generalizing the known methods of Burgers turbulence. The multifractal spectrum that we obtain significantly differs from the one of the adhesion model and conforms better to the laws of gravity. In this way, a unified theory of the large-scale structure of the universe seems to emerge. Furthermore, it explains our present knowledge of cosmic voids. A nonlacunar multifractal geometry can encompass three fundamental descriptions of the cosmic structure, namely, the web structure, hierarchical clustering, and halo distributions. The structures of matter clusters and cosmic voids in cosmological N-body simulations or the Sloan Digital Sky Survey are elucidated by means of multifractal geometry. The cosmic web structure is studied with the concepts and methods of fractal geometry, employing the adhesion model of cosmological dynamics as a basic reference. ![]()
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