Limitations of anthropic predictions for the cosmological constant $\Lambda$: Cosmic Heat Death of Anthropic Observers

Abstract

This paper investigates anthropic bounds on the vacuum energy $\Lambda$. We first consider the possibility of cosmic observers existing at any random time (including the future) for constant $\Lambda$, and take into account the suppression of new structure formation as the universe approaches its eternal DeSitter (DS) geometry. Structures that collapse prior to the era of $\Lambda$-domination will lose causal contact with our Hubble volume within a finite (short) conformal time ${\tau }_{\ast }$. Any remnants within our Hubble volume then suffer a cosmological heat death after the universe becomes DS. The probability for finding observers by random measurements in the volume bound by the DeSitter horizon is $P\simeq 0$, and it is a simple consequence of the information loss problem for eternal DS spaces resulting from the finite and constant value of its temperature $T_{DS}\simeq {\Lambda }^{-1/2}$ and entropy $S=3/(G\Lambda )$. By contrast, for geometries with $\Lambda =0$, structures can condense and entropy production can continue without bounds at any epoch. The probability of finding observers in $\Lambda =0$ geometries is thus overwhelming higher than in DS spaces. As a result, anthropic reasoning does not explain the small but nonzero vacuum energy observed in our universe. We also address the case where observers are considered only at a specially chosen time -- like the present epoch -- but relax the allowed values of starting density fluctuations and hence the redshift of galaxy formation. In this latter case, the bounds on a $\Lambda$ can be millions of times larger than previous estimates -- and the observed value. We thus conclude that anthropic reasoning has limited predictive power.

arXiv comment7pgs, published

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Cited by in corpus (14)

• Cosmological measure with volume averaging and the vacuum energy problem
• The Degree of Fine-Tuning in our Universe -- and Others
• The Born Rule Dies
• Predictions from Star Formation in the Multiverse
• Global-Local Duality in Eternal Inflation
• de Sitter equilibrium as a fundamental framework for cosmology
• Anthropic versus cosmological solutions to the coincidence problem
• Negative vacuum energy densities and the causal diamond measure
• Cosmological acceleration
• Effects of Inhomogeneity on the Causal Entropic prediction of Lambda
• Constraints on Vacuum Energy from Structure Formation and Nucleosynthesis
• Localization on the Landscape and Eternal Inflation
• An Infrared Divergence Problem in the cosmological measure theory and the anthropic reasoning
• Dark Matter Annihilations in the Causal Diamond