An Infrared Divergence Problem in the cosmological measure theory and the anthropic reasoning

TL;DR

This paper addresses the infrared divergence problem in cosmological measure theory related to the anthropic principle, proposing a solution using a singular runaway measure and Bayesian probabilities, and clarifies its stage-dependent nature.

Contribution

It introduces a Linde-Vanchurin singular runaway measure and applies the doomsday argument to resolve the infrared divergence issue in cosmological predictions.

Findings

IRD prediction can be avoided with the proposed measure.

The IRD problem occurs during prediction but not explanation.

The approach reconciles anthropic reasoning with measure theory.

Abstract

An anthropic principle has made it possible to answer the difficult question of why the observable value of cosmological constant ($\Lambda\sim 10^{-47}$ GeV${}^4$) is so disconcertingly tiny compared to predicted value of vacuum energy density $\rho_{SUSY}\sim 10^{12}$ GeV${}^4$. Unfortunately, there is a darker side to this argument, as it consequently leads to another absurd prediction: that the probability to observe the value $\Lambda=0$ for randomly selected observer exactly equals to 1. We'll call this controversy an infrared divergence problem. It is shown that the IRD prediction can be avoided with the help of a Linde-Vanchurin {\em singular runaway measure} coupled with the calculation of relative Bayesian probabilities by the means of the {\em doomsday argument}. Moreover, it is shown that while the IRD problem occurs for the {\em prediction stage} of value of $\Lambda$, it disappears at the {\em explanatory stage} when $\Lambda$ has already been measured by the observer.