Enhanced local-type inflationary trispectrum from a non-vacuum initial state

We compute the primordial trispectrum for curvature perturbations produced during cosmic ination in models with standard kinetic terms, when the initial quantum state is not necessarily the vacuum state. The presence of initial perturbations enhances the trispectrum amplitude for con guration in which one of the momenta, say k sub(3), is much smaller than the others, k sub(3) [Lt]k sub(1,2,4). For those squeezed con gurations the trispectrum acquires the so-called local form, with a scale dependent amplitude that can get values of order member of (k sub(1)/=k sub(3)) super(2). This amplitude could be larger than the prediction of the so-called Maldacena consistency relation by a factor as large as 10 super(6), and could reach the sensitivity of forthcoming observations, even for single-field inationary models.