Correlation functions in expanding universes

TL;DR

This work investigates how microscopic and macroscopic correlations evolve in expanding universes using a braneworld holographic framework. By embedding a braneworld in a $p$-brane gas geometry, the authors recover standard FLRW cosmology and compute time-dependent mutual information and two-point functions across inflationary and power-law expansion regimes using holographic prescriptions based on geodesic lengths and minimal surfaces. They find that mutual information between disjoint regions decays as a power law in time and vanishes when the separation exceeds a critical value, while two-point functions decay in time with a short-distance power law and a long-distance exponential screening that strengthens with matter density. These results provide a unified holographic picture of correlation dynamics in expanding spacetimes and yield concrete predictions for how expansion and background matter shape entanglement and local operator correlations.

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.

Figures (2)

• Figure 1: We depict entanglement entropies, $S_E (A)$ and $S_E (B)$, of two disjoint regions (left) and the entanglement entropy $S_E (A \cup B)$ of $A \cup B$ (right). Here, we assume that two disjoint regions with the same size $\bar{\rho}$ have a distance $2 d$.
• Figure 2: (a) Time evolution of a two-point function in FLRW cosmologies where we take $\Delta = |x_1 - x_2| = R =1$ and $z_h = 10$. (b) In the late time era, we numerically obtain $\gamma = 1$ for $w=0$, $\gamma = 4/3$ for $w=-1/3$, and $\gamma = 2$ for $w=-2/3$.