  We study non-Gaussian signatures on the cosmic microwave background (CMB)
radiation predicted within inflationary models with non-vacuum initial states
for cosmological perturbations. The model incorporates a privileged scale,
which implies the existence of a feature in the primordial power spectrum. This
broken-scale-invariant model predicts a vanishing three-point correlation
function for the CMB temperature anisotropies (or any other odd-numbered-point
correlation function) whilst an intrinsic non-Gaussian signature arises for any
even-numbered-point correlation function. We thus focus on the first
non-vanishing moment, the CMB four-point function at zero lag, namely the
kurtosis, and compute its expected value for different locations of the
primordial feature in the spectrum, as suggested in the literature to conform
to observations of large scale structure. The excess kurtosis is found to be
negative and the signal to noise ratio for the dimensionless excess kurtosis
parameter is equal to $| S/N | \simeq 4 \times 10^{-4}$, almost independently
of the free parameters of the model. This signature turns out to be
undetectable. We conclude that, subject to current tests, Gaussianity is a
generic property of single field inflationary models. The only uncertainty
concerning this prediction is that the effect of back-reaction has not yet been
properly incorporated. The implications for the trans-Planckian problem of
inflation are also briefly discussed.
