Predicting the cosmological constant from the causal entropic principle

Abstract

Abstract:We compute the expected value of the cosmological constant in our universe from the Causal Entropic Principle. Since observers must obey the laws of thermodynamics and causality, the principle asserts that physical parameters are most likely to be found in the range of values for which the total entropy production within a causally connected region is maximized. Despite the absence of more explicit anthropic criteria, the resulting probability distribution turns out to be in excellent agreement with observation. In particular, we find that dust heated by stars dominates the entropy production, demonstrating the remarkable power of this thermodynamic selection criterion. The alternative approach-weighting by the number of "observers per baryon"-is less well-defined, requires problematic assumptions about the nature of observers, and yet prefers values larger than present experimental bounds.

Predicting the cosmological constant with the scale-factor cutoff measure

“…In the latter case, the fit is better than that obtained in the "standard" calculations [24,25,26,27,28,29], which assume no time cutoff (this is equivalent to choosing a pocket-based measure on the multiverse). The causal patch measure also selects for smaller values of Λ providing, in the case of positive Λ, a fit to observation similar to that of the scale-factor cutoff [30]. Note, however, that the approach of Ref.…”

“…Note, however, that the approach of Ref. [30] used an entropy-based anthropic weighting (as opposed to the structure-formation-based approach used here) and that the distribution of negative Λ has not been studied in this measure.…”

“…The authors of Ref. [30] emphasize that the causal-patch measure gives a strong suppression for values of Λ more than about ten times the observed value, while anthropic constraints alone might easily allow values 1000 times larger than observed, depending on assumptions. Here, we calculate the distribution for Λ in the scale-factor cutoff measure, considering both positive and negative values of Λ, and compare our results with those of other approaches.…”

“…Most calculations of the distribution of Λ in the literature [24,25,26,27,28,29] do not explicitly specify the measure, but in fact correspond to using the pocket-based measure. The distribution of positive Λ in a causal-patch measure has also been considered [30]. The authors of Ref.…”

The geometry of large causal diamonds and the no-hair property of asymptotically de Sitter space–times

“…In a recent paper [1] we embarked on a quantitative study of causal diamonds, or Alexandrov open sets, which are beginning to play an increasingly important role in quantum gravity, for example in the approach via casual sets [2], in discussions of 'holography', and also of the probability of various observations in eternal inflation models (see [3] for a recent example and references to earlier work). The calculations in [1] were concerned with small causal diamonds, that is causal diamonds I + (p)∩I − (q) whose duration τ (p, q) 1 is small compared with the ambient curvature scale.…”