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 ψ, present during inflation, with a periodic potential given by v(ψ) = Λ 4 [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 Λ 4 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.

Reconstructing the Inflationary Landscape with Cosmological Data

“…If ψ has a potential ∆V (ψ) with a rich structure, then around horizon crossing ψ will fluctuate and diffuse across the potential barriers. After horizon crossing, it will be more probable to measure ψ at values that minimize ∆V (ψ) [20].Together, these two statements imply that the probability of measuring ζ is higher at those values sourced by ψ that minimize ∆V . This was shown in [16] for the particular case in which ψ is an axionlike field, with ∆V = Λ 4 [1 − cos(ψ/f )].…”

“…If ψ has a potential ∆V (ψ) with a rich structure, then around horizon crossing ψ will fluctuate and diffuse across the potential barriers. After horizon crossing, it will be more probable to measure ψ at values that minimize ∆V (ψ) [20].…”

“…Here, ψ k (t) is the mode function of a free massless field in a de Sitter spacetime. It turns out that σ 2 0 is time independent [20]. Performing the sum in Eq.…”

“…For instance, one approach to try and circumvent the aforementioned effects is to compute the transfer functions for a restricted multipole range, which can be done by modifying accordingly the sums in Eqs. (19) and (20), then to consider a filtered CMB map that only contains those contributions, and finally use Eq. (23) as before to obtain the reconstructed potential.…”

Non-Gaussian CMB and LSS statistics beyond polyspectra

“…However, one may conceive regimes characterised by interaction Lagrangians L int in which one is not allowed to disregard terms of higher powers in the fields. For instance, the field ψ may have a potential ∆V (ψ) displaying a rich structure within a wide field range ∆ψ [103]. In this case, the Lagrangian (A.8) can be rewritten as…”