2010/11/30 by Don N. Page
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Cosmology and Gravitation Theories #Quantum Mechanics and Applications #gr-qc #hep-th
paper · pdf · doi:10.1088/1475-7516/2011/03/031
published as JCAP 1103:031,2011 · 26 pages, LaTeX; discussion is added of how Agnesi weighting appears better than other recent measures
arxiv created 2011/02/24 · openalex publication_date 2011/03/21 · arxiv updated 2011/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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.