Abstract
We compute the primordial trispectrum for curvature
perturbations produced during cosmic inflation 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 configuration in which one of
the momenta, say k3, is much smaller than the others, k3 << k1,2,4. For those squeezed configurations the trispectrum
acquires the so-called local form, with a scale dependent amplitude
that can get values of order 
(k1/k3)2. This
amplitude could be larger than the prediction of the so-called
Maldacena consistency relation by a factor as large as 106, and
could reach the sensitivity of forthcoming observations, even for
single-field inflationary models.