Fractal dimension and negative pressure in cosmology

This study investigates the role of fractal dimensions in the evolution of large-scale structures within the Universe, focusing on the pressure-density relationship influenced by fractal geometry. Using a modified Van der Waals equation of state, one explores the behavior of cosmological clusters and the Universe, trying to understand how fractal dimensions may lead to either expansion or contraction phases. The results indicate that during the potential energy-dominated era, the fractal dimension is significantly high, suggesting a huge particle production and aligning with the rapid expansion during the inflationary epoch. Furthermore, the study proposes that the observed effects of dark energy/negative mass can be interpreted through the geometric properties of fractal dimensions, consistent with General Relativity principles in which the geometric properties of spacetime play a fundamental role.