Testing supersymmetric Higgs inflation with non-Gaussianity

We investigate multi-field signatures of the nonminimally coupled supersymmetric Higgs inflation-type cosmological scenario, focusing on the two-field Higgs-lepton inflation model as a concrete example. This type of inflationary model is realized in a theory beyond the Standard Model embedded in supergravity with a noncanonical K\"{a}hler potential. We employ the backward $\delta N$ formalism to compute cosmological observables, including the scalar and tensor power spectra, the spectral indices, the tensor-to-scalar ratio and the local-type nonlinearity parameter. The trajectory of the inflaton is controlled by the initial conditions of the inflaton as well as by the coefficients in the K\"{a}hler potential. We analyze the bispectrum of the primordial fluctuations when the inflaton trajectory deviates from a straight line, and obtain constraints on the noncanonical terms of the K\"{a}hler potential using the Planck satellite data. Our analysis represents a concrete particle phenomenology-based case study of inflation in which primordial non-Gaussianities can reveal aspects of supergravity.