Vacuum Selection on Axionic Landscapes

TL;DR

This paper analyzes the distribution of minima in multi-field axionic landscapes, revealing that dynamical processes favor certain minima over naive expectations, with implications for inflation and the cosmological constant problem.

Contribution

It provides a combined numerical and analytical study of minima distribution in axionic landscapes, highlighting the limitations of random matrix theory in this context.

Findings

Dynamical selection favors low-lying minima.

Trajectories often get trapped in nearby minima.

Analytic estimates from random matrix theory are insufficient.

Abstract

We compute the distribution of minima that are reached dynamically on multi-field axionic landscapes, both numerically and analytically. Such landscapes are well suited for inflationary model building due to the presence of shift symmetries and possible alignment effects (the KNP mechanism). The resulting distribution of dynamically reached minima differs considerably from the naive expectation based on counting all vacua. These differences are more pronounced in the presence of many fields due to dynamical selection effects: while low lying minima are preferred as fields roll down the potential, trajectories are also more likely to get trapped by one of the many nearby minima. We show that common analytic arguments based on random matrix theory in the large $D$-limit to estimate the distribution of minima are insufficient for quantitative arguments pertaining to the dynamically reached ones. This discrepancy is not restricted to axionic potentials. We provide an empirical expression for the expectation value of such dynamically reached minimas' height and argue that the cosmological constant problem is not alleviated in the absence of anthropic arguments. We further comment on the likelihood of inflation on axionic landscapes in the large D-limit.