Spacetime Average Density (SAD) Cosmological Measures

TL;DR

This paper introduces two new spacetime average density measures, MAD and BAD, to address the cosmological measure problem, avoiding infinities and Boltzmann brain domination, and aligning with key observations like a positive cosmological constant.

Contribution

The paper proposes two novel SAD measures, MAD and BAD, that restrict to finite spacetime regions to solve measure problems in cosmology.

Findings

MAD and BAD avoid Boltzmann brain domination

They produce finite observation probabilities

Results are consistent with observed positive cosmological constant

Abstract

The measure problem of cosmology is how to obtain normalized probabilities of observations from the quantum state of the universe. This is particularly a problem when eternal inflation leads to a universe of unbounded size so that there are apparently infinitely many realizations or occurrences of observations of each of many different kinds or types, making the ratios ambiguous. There is also the danger of domination by Boltzmann Brains. Here two new Spacetime Average Density (SAD) measures are proposed, Maximal Average Density (MAD) and Biased Average Density (BAD), for getting a finite number of observation occurrences by using properties of the Spacetime Average Density (SAD) of observation occurrences to restrict to finite regions of spacetimes that have a preferred beginning or bounce hypersurface. These measures avoid Boltzmann brain domination and appear to give results consistent with other observations that are problematic for other widely used measures, such as the observation of a positive cosmological constant.