Agnesi Weighting for the Measure Problem of Cosmology
arXiv:1011.4932 · doi:10.1088/1475-7516/2011/03/031
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.
arXiv comment26 pages, LaTeX; discussion is added of how Agnesi weighting appears better than other recent measures
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