Age-dependent decay in the landscape

The picture of the “multiverse” arising in diverse cosmological scenarios involves transitions between metastable vacuum states. It was pointed out by Krauss and Dent that the transition rates decrease at very late times, leading to a dependence of the transition probability between vacua on the age of each vacuum region. I investigate the implications of this non-Markovian, age-dependent decay on the global structure of the spacetime in landscape scenarios. I show that the fractal dimension of the eternally inflating domain is precisely equal to 3, instead of being slightly below 3, which is the case in scenarios with purely Markovian, age-independent decay. I develop a complete description of a non-Markovian landscape in terms of a nonlocal master equation. Using this description I demonstrate by an explicit calculation that, under some technical assumptions about the landscape, the probabilistic predictions of our position in the landscape are essentially unchanged, regardless of the measure used to extract these predictions. I briefly discuss the physical plausibility of realizing non-Markovian vacuum decay in cosmology in view of the possible decoherence of the metastable quantum state.

Figure 1

First steps in the construction of a random Sierpiński carpet with $N=5$ and $q=5/6$.