Anthropic prediction for a large multi-jump landscape

TL;DR

This paper extends previous work on anthropic predictions of the cosmological constant by analyzing a large multi-jump landscape model, showing that the prior distribution can be effectively flat under certain conditions, validating anthropic predictions.

Contribution

It introduces a large multi-jump landscape model and demonstrates conditions under which the prior distribution remains effectively flat, supporting anthropic predictions.

Findings

For large jump size parameter c, the distribution is effectively flat.

For small c, the distribution may not be smooth.

Supports the validity of anthropic predictions under certain landscape conditions.

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.