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

TL;DR

This paper argues that anthropic reasoning cannot reliably predict the small positive value of the cosmological constant due to cosmic heat death and information loss in de Sitter space, challenging its explanatory power.

Contribution

It demonstrates that cosmic heat death and information loss in de Sitter space limit the predictive power of anthropic bounds on the cosmological constant.

Findings

Probability of observers in de Sitter space is nearly zero due to heat death.

Structures and entropy production are unbounded in zero cosmological constant universe.

Anthropic bounds on $\\Lambda$ can be significantly larger when considering specific epochs.

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.