Correlation functions in expanding universes

Abstract

By using the braneworld model, we investigate the time evolution of microscopic and macroscopic correlations in expanding universes. To describe the FLRW cosmologies in the holographic setup, we take into account a braneworld moving in the $p$-brane gas geometry, where the radial motion of the braneworld determines the cosmology in the braneworld. We show that the braneworld model reproduces the standard cosmology exactly. In this braneworld model, we investigate the time-dependent mutual information between two disjoint macroscopic subregions and the time-dependent two-point functions in the expanding universes. We find that the mutual information becomes zero when the distance between two subregions is slightly larger than the subsystem size. We also find that it decreases as time and the density of matter increase. On the other hand, the microscopic two-point function in the short-distance limit decreases by a power law, while it is exponentially suppressed in the long-distance limit due to the screening effect. In addition, we find that the two-point function is also suppressed by a power law with time.