# Axion excursions of the landscape during inflation

## TL;DR

This paper analyzes how quantum fluctuations of an axion field during inflation can lead to a non-Gaussian, multimodal distribution of field values across different universe patches, with significant cosmological implications.

## Contribution

It provides a first-order in $\Lambda^4$ calculation of the axion field's probability distribution during inflation, revealing non-Gaussian, multimodal features due to tunneling effects.

## Key findings

- Probability distribution is multimodal and non-Gaussian.
- Different universe patches have varied axion field values.
- Implications for isocurvature fluctuations, multiverse, and dark matter signatures.

## Abstract

Because of their quantum fluctuations, axion fields had a chance to experience field excursions traversing many minima of their potentials during inflation. We study this situation by analyzing the dynamics of an axion-spectator field $\psi$, present during inflation, with a periodic potential given by $v(\psi) = \Lambda^4 [1 - \cos (\psi / f)]$. By assuming that the vacuum expectation value of the field is stabilized at one of its minima, say $\psi = 0$, we compute every $n$-point correlation function of $\psi$ up to first order in $\Lambda^4$ using the in-in formalism. This computation allows us to identify the distribution function describing the probability of measuring $\psi$ at a particular amplitude during inflation. Because $\psi$ is able to tunnel between the barriers of the potential, we find that the probability distribution function consists of a non-Gaussian multimodal distribution such that the probability of measuring $\psi$ at a minimum of $v(\psi)$ different from $\psi=0$ increases with time. As a result, at the end of inflation, different patches of the Universe are characterized by different values of the axion field amplitude, leading to important cosmological phenomenology: (a) Isocurvature fluctuations induced by the axion at the end of inflation could be highly non-Gaussian. (b) If the axion defines the strength of standard model couplings, then one is led to a concrete realization of the multiverse. (c) If the axion corresponds to dark matter, one is led to the possibility that, within our observable Universe, dark matter started with a nontrivial initial condition, implying novel signatures for future surveys.