Emergent Dynamics at Cosmological Scales

In this paper, I investigated the emergent dynamics in the Newtonian limit by modeling a toy model of the universe with $N$ masses coupled by gravity incorporating the cosmological constant. The dynamics are given by the equation of the Kuramoto-like form. This many-body system is drastically simpler by using a mean field approach. The equilibrium solution of the equation is consistent with the usual Milgrom’s empirical law. It turns out that the state of the universe at large scales enters local dynamics in local small systems, such as galaxies. However, in the context of general relativity, gravity is described within a geometric framework. Thus, I constructed a geometric dynamical equation for the gravitational system, which describes a geometric flow.