Agnesi Weighting for the Measure Problem of Cosmology
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.
Keywords
Cite
@article{arxiv.1011.4932,
title = {Agnesi Weighting for the Measure Problem of Cosmology},
author = {Don N. Page},
journal= {arXiv preprint arXiv:1011.4932},
year = {2011}
}
Comments
26 pages, LaTeX; discussion is added of how Agnesi weighting appears better than other recent measures