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We show that the shape of the inflationary landscape potential may be constrained by analyzing cosmological data. The quantum fluctuations of fields orthogonal to the inflationary trajectory may have probed the structure of the local landscape potential, inducing non-Gaussianity (NG) in the primordial distribution of the curvature perturbations responsible for the cosmic microwave background (CMB) anisotropies and our Universe's large-scale structure. The resulting type of NG (tomographic NG) is determined by the shape of the landscape potential, and it cannot be fully characterized by 3- or 4-point correlation functions. Here we deduce an expression for the profile of this probability distribution function in terms of the landscape potential, and we show how this can be inverted in order to reconstruct the potential with the help of CMB observations. While current observations do not allow us to infer a significant level of tomographic NG, future surveys may improve the possibility of constraining this class of primordial signatures. [ABSTRACT FROM AUTHOR]