Age-dependent decay in the landscape

Abstract

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 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.

10 pages, RevTeX4, 1 figure included. Clarification of approximation used, conclusions weakened

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Cited by in corpus (6)

• Cosmological implications of the transition from the false vacuum to the true vacuum state
• Disorder on the landscape
• Properties of the false vacuum as the quantum unstable state
• A universe born in a metastable false vacuum state needs not die
• Decoherence delays false vacuum decay
• Cosmological "constant" in a universe born in the metastable false vacuum state