The Resolution of the Gauge Problem of Cosmology provides Insight into the Formation of the First Structures in the Universe

Résumé : This paper presents a novel approach to four fundamental problems in the field of cosmological perturbation theory. Firstly, the issue of gauge dependence has been addressed by demonstrating the existence of unique and gauge-invariant quantities corresponding to the actual perturbations. Secondly, the formation of primordial structures after decoupling of matter and radiation is dependent on the existence of local fluid flows resulting from local pressure gradients. To take pressure gradients into account, it is necessary to consider both the energy density and the particle number density. Thirdly, the novel relativistic perturbation theory applies to an open, flat, and closed Friedmann-Lema\^itre-Robertson-Walker universe. The derivation of the novel perturbation theory definitively reveals the inherent limitations of Newtonian gravitation as a framework for investigating cosmological density perturbations. Finally, the application of the perturbation theory to a flat universe demonstrates that, prior to decoupling, perturbations in both Cold Dark Matter and ordinary matter are coupled to perturbations in radiation. Therefore, the universe's earliest structures formed only after decoupling, at which point local nonadiabatic random pressure fluctuations became a significant factor. Negative nonadiabatic pressure fluctuations resulted in a brief, rapid growth of density fluctuations until the total pressure fluctuations became positive. In contrast, positive nonadiabatic pressure fluctuations led to the formation of voids. Perturbations with masses about $2.2\times10^{4}\,\text{M}_\odot$ became nonlinear already $60$ million years after the Big Bang, and perturbations with masses between $6.7\times10^2\,\text{M}_\odot$ and $1.2\times10^6\,\text{M}_\odot$ became nonlinear within about $600$ million years.