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