Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Anthropic prediction for Lambda and the Q catastrophe

Jaume Garriga, Alexander Vilenkin

TL;DR

The paper analyzes how anthropic reasoning predicts the cosmological constant Λ and the density-perturbation amplitude Q when both are allowed to vary in a multiverse with eternal inflation. It shows that the joint distribution P(Λ,Q) factorizes into a largely universal y-distribution, with $y=Λ/(ρ_m σ_G^3)$, and a P(Q) that depends sensitively on the perturbation mechanism (inflaton vs curvaton) and the assumed priors. In inflaton-based scenarios, P(Q) tends to favor extreme values, producing large-$Q$ or small-$Q$ catastrophes depending on the specific prior, whereas curvaton-type models decouple Q from inflation and can avoid these catastrophes, potentially aligning with the observed $Q\sim 10^{-5}$. The work emphasizes unresolved issues about prior probabilities in an eternally inflating multiverse and suggests that multi-component curvaton models or more general priors can mitigate catastrophes, with the robust y-prediction providing a testable anchor for anthropic reasoning.

Abstract

We discuss probability distributions for the cosmological constant Lambda and the amplitude of primordial density fluctuations Q in models where they both are anthropic variables. With mild assumptions about the prior probabilities, the distribution P(Lambda,Q) factorizes into two independent distributions for the variables Q and $y \propto Λ/Q^3$. The distribution for y is largely model-independent and is in a good agreement with the observed value of y. The form of P(Q) depends on the origin of density perturbations. If the perturbations are due to quantum fluctuations of the inflaton, then P(Q) tends to have an exponential dependence on Q, due to the fact that in such models Q is correlated with the amount of inflationary expansion. For simple models with a power-law potential, P(Q) is peaked at very small values of Q, far smaller than the observed value of 10^{-5}. This problem does not arise in curvaton-type models, where the inflationary expansion factor is not correlated with Q.

Anthropic prediction for Lambda and the Q catastrophe

TL;DR

The paper analyzes how anthropic reasoning predicts the cosmological constant Λ and the density-perturbation amplitude Q when both are allowed to vary in a multiverse with eternal inflation. It shows that the joint distribution P(Λ,Q) factorizes into a largely universal y-distribution, with , and a P(Q) that depends sensitively on the perturbation mechanism (inflaton vs curvaton) and the assumed priors. In inflaton-based scenarios, P(Q) tends to favor extreme values, producing large- or small- catastrophes depending on the specific prior, whereas curvaton-type models decouple Q from inflation and can avoid these catastrophes, potentially aligning with the observed . The work emphasizes unresolved issues about prior probabilities in an eternally inflating multiverse and suggests that multi-component curvaton models or more general priors can mitigate catastrophes, with the robust y-prediction providing a testable anchor for anthropic reasoning.

Abstract

We discuss probability distributions for the cosmological constant Lambda and the amplitude of primordial density fluctuations Q in models where they both are anthropic variables. With mild assumptions about the prior probabilities, the distribution P(Lambda,Q) factorizes into two independent distributions for the variables Q and . The distribution for y is largely model-independent and is in a good agreement with the observed value of y. The form of P(Q) depends on the origin of density perturbations. If the perturbations are due to quantum fluctuations of the inflaton, then P(Q) tends to have an exponential dependence on Q, due to the fact that in such models Q is correlated with the amount of inflationary expansion. For simple models with a power-law potential, P(Q) is peaked at very small values of Q, far smaller than the observed value of 10^{-5}. This problem does not arise in curvaton-type models, where the inflationary expansion factor is not correlated with Q.

Paper Structure

This paper contains 10 sections, 42 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Anthropic prediction for $\Lambda$
  3. Variable $Q$
  4. The large $Q$ catastrophe
  5. The problem of the prior
  6. A conjecture for a more general case
  7. The small-$Q$ catastrophe
  8. Curvaton-type models
  9. Evading the large-$Q$ catastrophe
  10. Conclusions

Figures (1)

  • Figure 1: The spacetime structure of a pocket universe.