  Deviations from the Bunch-Davies vacuum during an inflationary period can
leave a testable imprint on the higher-order correlations of the CMB and large
scale structures in the Universe. The effect is particularly pronounced if the
statistical non-Gaussianity is inherently large, such as in models of inflation
with a small speed of sound, e.g. DBI. First reviewing the motivations for a
modified vacuum, we calculate the non-Gaussianity for a general action with a
small speed of sound. The shape of its bispectrum is found to most resemble the
'orthogonal' or 'local' templates depending on the phase of the Bogolyubov
parameter. In particular, for DBI models of inflation the bispectrum can have a
profound 'local' template feature, in contrast to previous results. Determining
the projection into the observational templates allows us to derive constraints
on the absolute value of the Bogolyubov parameter. In the small sound speed
limit, the derived constraints are generally stronger than the existing
constraint derived from the power spectrum. The bound on the absolute value of
the Bogolyubov parameter ranges from the 10^-6 to the 10^-3 level for
H/\Lambda_c = 10^-3, depending on the specific details of the model, the sound
speed and the phase of the Bogolyubov parameter.
