Cycles in the multiverse

Eternal inflation is a seemingly generic consequence of theories that give rise to accelerated expansion of the universe and possess multiple vacuum states. Making predictions in an eternally inflating universe is notoriously difficult because one must compare infinite quantities, and a wide variety of regulating procedures yield radically different results. This is the measure problem of eternal inflation. In this paper, we analyze models of eternal inflation which allow for the possibility of cyclic bubble universes: in each bubble, standard cosmological evolution is replayed over and over again. Eternal inflation can generically arise in cyclic models that include a dark energy dominated phase. In such models, several problematic consequences of certain regulating procedures, such as the youngness and Boltzmann brain problems, are substantially alleviated. We discuss the implications for making predictions in cyclic models, as well as some general implications for understanding the measure problem in eternal inflation.

Figure 1

The cyclic/inflationary multiverse.

Figure 2

A potential that gives rise to slow-roll eternal inflation and cyclic cosmologies. The inflating phase near the local maximum can exit either to a decompactified phase (left) or a cyclic pocket universe (right).

Figure 3

The cyclic universe incorporating false vacuum eternal inflation.

Figure 4

A comparison of the solutions to Eq. (6) (solid lines) and Eq. (8) (dashed lines) for $t_D=6H_F^{-1}$, $t_R=2H_F^{-1}$, ${\Gamma }_{DF}=0.1H_F$. The continuum approximation works very well at estimating the average volume in each phase.

Figure 5

A comparison of the solutions to Eq. (10) (solid lines) and Eq. (13) (dashed lines) for the same parameters used in Fig. 4, but where only 50% of the volume makes it through the crunch/bang transition ($p=0.5$). We exclude from this plot the volume fraction in the regions that have crunched (which dominates the volume fraction at late times). Again, the continuum approximation works well at determining the volume fractions.

Figure 6

Relationships between the different vacua that we consider in this section.

Figure 7

The tunneling path from a false vacuum (on the right) to the two-field ekpyrotic phase (on the left).

Figure 8

A sketch of the effective potential defined in Eq. (a8).