Vacuum statistics and stability in axionic landscapes

TL;DR

This paper studies the distribution and stability of vacua in axionic landscapes, introducing an efficient algorithm for tunneling calculations and exploring how vacuum stability correlates with energy density and the number of fields.

Contribution

The authors develop a fast, accurate algorithm for evaluating tunneling actions in axionic landscapes and analyze the statistical properties of vacuum stability and distribution.

Findings

Vacuum stability increases as energy density decreases.

Probability of large tunneling actions declines as a power law, not exponentially.

Number of stable vacua grows exponentially with the number of fields.

Abstract

We investigate vacuum statistics and stability in random axionic landscapes. For this purpose we developed an algorithm for a quick evaluation of the tunneling action, which in most cases is accurate within 10%. We find that stability of a vacuum is strongly correlated with its energy density, with lifetime rapidly growing as the energy density is decreased. The probability $P(B)$ for a vacuum to have a tunneling action $B$ greater than a given value declines as a slow power law in $B$. This is in sharp contrast with the studies of random quartic potentials, which found a fast exponential decline of $P(B)$. Our results suggest that the total number of relatively stable vacua (say, with $B> 100$) grows exponentially with the number of fields $N$ and can get extremely large for $N\gtrsim 100$. The problem with this kind of model is that the stable vacua are concentrated near the absolute minimum of the potential, so the observed value of the cosmological constant cannot be explained without fine-tuning. To address this difficulty, we consider a modification of the model, where the axions acquire a quadratic mass term, due to their mixing with 4-form fields. This results in a larger landscape with a much broader distribution of vacuum energies. The number of relatively stable vacua in such models can still be extremely large.