Anthropic Distribution for Cosmological Constant and Primordial Density Perturbations

TL;DR

This paper examines how variations in primordial density perturbations across different universes affect the likelihood of observing our universe's cosmological constant, using toy inflationary models to derive probability distributions.

Contribution

It introduces a framework for analyzing the anthropic principle with variable primordial perturbations and assesses the probability of our universe's parameters within this context.

Findings

Likelihood of living in a typical universe is generally small.

Probability distributions depend on toy inflationary models.

Anthropic explanation for the cosmological constant is less probable under these models.

Abstract

The anthropic principle has been proposed as an explanation for the observed value of the cosmological constant. Here we revisit this proposal by allowing for variation between universes in the amplitude of the scale-invariant primordial cosmological density perturbations. We derive a priori probability distributions for this amplitude from toy inflationary models in which the parameter of the inflaton potential is smoothly distributed over possible universes. We find that for such probability distributions, the likelihood that we live in a typical, anthropically-allowed universe is generally quite small.