Eternal inflation, bubble collisions, and the persistence of memory

Abstract

A ``bubble universe'' nucleating in an eternally inflating false vacuum will experience, in the course of its expansion, collisions with an infinite number of other bubbles. In an idealized model, we calculate the rate of collisions around an observer inside a given reference bubble. We show that the collision rate violates both the homogeneity and the isotropy of the bubble universe. Each bubble has a center which can be related to ``the beginning of inflation'' in the parent false vacuum, and any observer not at the center will see an anisotropic bubble collision rate that peaks in the outward direction. Surprisingly, this memory of the onset of inflation persists no matter how much time elapses before the nucleation of the reference bubble.

Figures (3)

• Figure 1: Region in grey shade, ${\cal V}_4(r_0)$ can nucleate bubbles which will be within the distance $r_0$ from the origin (on the flat surface $t=0$). Here, we assume that the point $r=t=0$ is still in false vacuum. Region in horizontal stripes, $V_4(\xi,\tau)$, can nucleate bubbles which will collide with ours, and which will be visible within a coordinate radius $\xi$ from the origin (on the $\tau=const.$ hypersurface). Here, we assume that the center point $\xi=0$ has not yet been hit by any bubble.
• Figure 2: Conformal diagram of a bubble in a de Sitter space. The relevant 4-volume to the past of a sphere of radius $\xi$ around the origin is shaded in grey.
• Figure 3: Same as in Fig. \ref{['2j']}, but now the "true" vacuum inside the bubble is of lower energy. For simplicity, we take it to be Minkowski, although this is not essential. In this case, the shaded area corresponding to the 4-volume available for the nucleation of bubbles which will hit a distance $\Delta\xi$ away from the point of observation, is finite. All we need is that the backward light cone from the point of observation reaches the point $\chi=0$ at some time in the past. This will happen if the cosmological horizon at the time of observation is many times larger than the Hubble size during inflation. Formally, we do not need a cut-off initial surface, and seemingly we obtain a finite answer which respects $O(3,1)$ invariance. However, we know that physically some initial conditions are needed. These look different to different observers in the FRW congruence, which leads to anisotropies in the distribution of bubbles.