Anthropic prediction in a large toy landscape

Abstract

The successful anthropic prediction of the cosmological constant depends crucially on the assumption of a flat prior distribution. However, previous calculations in simplified landscape models showed that the prior distribution is staggered, suggesting a conflict with anthropic predictions. Here we analytically calculate the full distribution, including the prior and anthropic selection effects, in a toy landscape model with a realistic number of vacua, $N\sim 10^{500}$. We show that it is possible for the fractal prior distribution we find to behave as an effectively flat distribution in a wide class of landscapes, depending on the regime of parameter space. Whether or not this possibility is realized depends on presently unknown details of the landscape.

13 pages

References in corpus (9)

• Sinks in the Landscape, Boltzmann Brains, and the Cosmological Constant Problem
• Holographic probabilities in eternal inflation
• Probabilities in the Bousso-Polchinski multiverse
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• Freak observers and the measure of the multiverse
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• Boundary definition of a multiverse measure
• Search Optimization, Funnel Topography, and Dynamical Criticality on the String Landscape
• Accessibility Measure for Eternal Inflation: Dynamical Criticality and Higgs Metastability
• Negative vacuum energy densities and the causal diamond measure
• Early-Time Measure in Eternal Inflation
• Anthropic prediction for a large multi-jump landscape
• Reheating-volume measure in the landscape
• Bayesian Reasoning in Eternal Inflation: A Solution to the Measure Problem
• Phenomenology of the CAH+ measure
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• Multi-Vacuum Initial Conditions and the Arrow of Time
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• The Roche-Lobe Radius in Newtonian and Non-Newtonian Gravity