Axion excursions of the landscape during inflation
AbstractBecause 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 ψ, present during inflation, with a periodic potential given by v(ψ)=Λ4[1-cos(ψ/f)]. By assuming that the vacuum expectation value of the field is stabilized at one of its minima, say, ψ=0, we compute every n-point correlation function of ψ up to first order in Λ4 using the in-in formalism. This computation allows us to identify the distribution function describing the probability of measuring ψ at a particular amplitude during inflation. Because ψ 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 ψ at a minimum of v(ψ) different from ψ=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.