Abstract
We compute the fourth order action in perturbation theory for scalar and second order tensor perturbations for a minimally coupled single field inflationary model, where the inflaton's Lagrangian is a general function of the field's value and its kinetic energy. We obtain the fourth order interaction Hamiltonian in two gauges, the comoving gauge and the uniform curvature gauge. Using the comoving gauge action we calculate the trispectrum at leading order in slow roll, finding agreement with a previously known result in the literature. We point out that, in general, to obtain the correct leading order trispectrum one cannot ignore second order tensor perturbations as previously done by others. The next-to-leading order corrections may become detectable depending on the shape, and we provide the necessary formalism to calculate them.
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