Landscape tomography through primordial non-Gaussianity

Abstract

In this paper, we show how the structure of the landscape potential of the primordial Universe may be probed through the properties of the primordial density perturbations responsible for the origin of the cosmic microwave background anisotropies and the large-scale structure of our Universe. Isocurvature fields -fields orthogonal to the inflationary trajectory-may have fluctuated across the barriers separating local minima of the landscape potential during inflation. We analyze how this process could have impacted the evolution of the primordial curvature perturbations. If the typical distance separating consecutive minima of the landscape potential and the height of the potential barriers are smaller than the Hubble expansion rate parametrizing inflation, the probability distribution function of isocurvature fields becomes non-Gaussian due to the appearance of bumps and dips associated with the structure of the potential. We show that this non-Gaussianity can be transferred to the statistics of primordial curvature perturbations if the isocurvature fields are coupled to the curvature perturbations. The type of non-Gaussian structure that emerges in the distribution of curvature perturbations cannot be fully probed with the standard methods of polyspectra; instead, the probability distribution function is needed. The latter is obtained by summing all the n-point correlation functions. To substantiate our claims, we offer a concrete model consisting of an axionlike isocurvature perturbation with a sinusoidal potential and a linear derivative coupling between the isocurvature and curvature field. In this model, the probability distribution function of the curvature perturbations consists of a Gaussian function with small superimposed oscillations reflecting the isocurvature axion potential.

A tip for landscape riders: multi-field inflation can fulfill the swampland distance conjecture

“…Last but not least, non-geodesic trajectories in multi-field spaces also induce the transfer of non-Gaussianity from the isocurvature field to the curvature perturbation, at a rate that depends on the values ofμ and λ [78][79][80][81][82]. This means that non-Gaussianity observations would allow us to place additional constraints on the parameter space studied in this work.…”

Non-Gaussian CMB and LSS statistics beyond polyspectra

“…Ref. [46]) and use Eqs. (4.8) and (4.10) as a template without having to refer to moments; and finally, 3) consider statistical estimators on the LSS dataset probing the primordial PDF via the counting scheme implied by Eq.…”

“…ψ 3 + · · · ; instead, one has to perform perturbative computations where information about the entire potential ∆V is kept under control. As shown in [46,47], as long as ∆V /H 4 ≪ 1, it is indeed possible to compute every n-point correlation function for ζ and to derive its probability distribution function, P(ζ). Remarkably, this PDF turns out to be given by a Gaussian profile with small non-Gaussian corrections determined by the shape of the landscape potential ∆V .…”

“…In the present article, we wish to argue in favour of reconstructing the full function F NG of Eq. (1.1) from CMB and LSS observations without necessarily assuming a hierarchical dependence of the functions F n on a given coupling constant g. We posit that the search for non-Gaussianity focused on low n-point correlation functions may miss the existence of richer types of statistics [44][45][46][47][48] that we may be unable to predict by following standard perturbation theory techniques. For example, in App.…”

“…Certainly, one cannot discard the possibility of having potentials ∆V (ψ) characterised by a rich structure (i.e. with consecutive minima separated by field distances smaller than the Hubble expansion rate during inflation) in which case the bispectrum would not constitute an efficient tool to parametrise non-Gaussianity [46,47]. A simple example of this, related to the presence of an axionic isocurvature direction, is…”