Anthropic prediction for Lambda and the Q catastrophe

TL;DR

This paper explores the probability distributions of the cosmological constant and primordial density fluctuations, showing how different inflation models influence their expected values and align with observations.

Contribution

It introduces a model-independent distribution for the variable y related to Lambda and Q, and compares how different inflation scenarios affect the distribution of Q.

Findings

Distribution P(y) aligns with observed y value.

Power-law inflation models favor smaller Q than observed.

Curvaton models avoid the small Q problem.

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 $y \propto \Lambda/Q^3$. 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.