Agnesi weighting for the measure problem of cosmology

Abstract

The measure problem of cosmology is how to assign normalizedprobabilities to observations in a universe so large that it may havemany observations occurring at many different spacetime locations. Ihave previously shown how the Boltzmann brain problem (that observationsarising from thermal or quantum fluctuations may dominate over ordinaryobservations if the universe expands sufficiently and/or lasts longenough) may be ameliorated by volume averaging, but that still leavesproblems if the universe lasts too long. Here a solution is proposedfor that residual problem by a simple weighting factor 1/(1+t2) tomake the time integral convergent. The resulting Agnesi measure appearsto avoid problems other measures may have with vacua of zero or negativecosmological constant.