Anthropic prediction for a large multi-jump landscape

Abstract

The assumption of a flat prior distribution plays a critical role in the anthropic prediction of the cosmological constant. In a previous paper we analytically calculated the distribution for the cosmological constant, including the prior and anthropic selection effects, in a large toy ``single-jump'' landscape model. We showed that it is possible for the fractal prior distribution we found to behave as an effectively flat distribution in a wide class of landscapes, but only if the single jump size is large enough. We extend this work here by investigating a large ($N\sim 10^{500}$) toy ``multi-jump'' landscape model. The jump sizes range over three orders of magnitude and an overall free parameter $c$ determines the absolute size of the jumps. We will show that for ``large'' $c$ the distribution of probabilities of vacua in the anthropic range is effectively flat, and thus the successful anthropic prediction is validated. However, we argue that for small $c$, the distribution may not be smooth.

33 pages, 7 figures Minor revisions made and references added. arXiv admin note: substantial text overlap with arXiv:0705.2562

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• Reheating-volume measure in the landscape
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• Multiverse rate equation including bubble collisions
• An Infrared Divergence Problem in the cosmological measure theory and the anthropic reasoning