Eur. Phys. J. C (2011) 71: 1740
https://doi.org/10.1140/epjc/s10052-011-1740-0

Regular Article - Theoretical Physics

An infrared divergence in the cosmological measure theory and the anthropic reasoning

¹ Department of Theoretical Physics, Baltic Federal University of I. Kant, 14, Nevsky st., Kaliningrad, 236041, Russia
² Department of Mathematics, University of Missouri, Columbia, CO, 65201, USA

^* e-mail: artyom_yurov@mail.ru

Received: 24 June 2011
Revised: 30 July 2011
Published online: 28 October 2011

Abstract

An anthropic principle has made it possible to answer the difficult question of why the observable value of cosmological constant (Λ∼10⁻⁴⁷ GeV⁴) is so disconcertingly tiny compared to the predicted value of vacuum energy density ρ _SUSY∼10¹² GeV⁴. Unfortunately, there is a darker side to this argument; being combined with the cosmic heat death scenario, it consequently leads to another absurd prediction: the probability of randomly selected observer observing Λ=0 ends up being exactly equal to 1. We shall call this controversy an infrared divergence problem. It is shown that the IRD prediction can be avoided with the help of a singular runaway measure coupled with the calculation of relative Bayesian probabilities by the means of the doomsday argument. Moreover, it is shown that while the IRD problem occurs for the prediction stage of value of Λ, it disappears at the explanatory stage when Λ has already been measured by the observer.