Agnesi Weighting for the Measure Problem of Cosmology

TL;DR

This paper introduces the Agnesi measure, a new weighting approach for the cosmological measure problem, which helps assign probabilities to observations in an infinitely large universe and addresses issues like the Boltzmann brain problem.

Contribution

The paper proposes the Agnesi weighting factor 1/(1+t^2) as a novel solution to the measure problem, ensuring convergence and resolving issues with vacua of zero or negative cosmological constant.

Findings

The Agnesi measure avoids divergence in probability calculations.

It mitigates the Boltzmann brain problem in cosmology.

It effectively handles vacua with zero or negative cosmological constant.

Abstract

The measure problem of cosmology is how to assign normalized probabilities to observations in a universe so large that it may have many observations occurring at many different spacetime locations. I have previously shown how the Boltzmann brain problem (that observations arising from thermal or quantum fluctuations may dominate over ordinary observations if the universe expands sufficiently and/or lasts long enough) may be ameliorated by volume averaging, but that still leaves problems if the universe lasts too long. Here a solution is proposed for that residual problem by a simple weighting factor 1/(1+t^2) to make the time integral convergent. The resulting Agnesi measure appears to avoid problems other measures may have with vacua of zero or negative cosmological constant.