Axion excursions of the landscape during inflation

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 $\ddot{I}ˆ$, present during inflation, with a periodic potential given by $v(\ddot{I}ˆ)=\hat{I}{›}^4[1-\cos (\ddot{I}ˆ/f)]$. By assuming that the vacuum expectation value of the field is stabilized at one of its minima, say $\ddot{I}ˆ=0$, we compute every $n$-point correlation function of $\ddot{I}ˆ$ up to first order in $\hat{I}{›}^4$ using the in-in formalism. This computation allows us to identify the distribution function describing the probability of measuring $\ddot{I}ˆ$ at a particular amplitude during inflation. Because $\ddot{I}ˆ$ 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 $\ddot{I}ˆ$ at a minimum of $v(\ddot{I}ˆ)$ different from $\ddot{I}ˆ=0$ 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.

7 pages, 2 figures. v2: references added, improved discussion