  Prior to recombination, Silk damping causes the dissipation of energy from
acoustic waves into the monopole of the Cosmic Microwave Background (CMB),
resulting in spectral distortions. These can be used to probe the primordial
scalar power spectrum on smaller scales than it is possible with CMB
anisotropies. An enhancement of power on these scales is nevertheless required
for the resulting distortions to be detectable by future experiments like
PIXIE. In this paper, we examine all 49 single-field inflation models listed by
Martin et al. in the Encyclopaedia Inflationaris [1] and find that only one of
these may lead to a detectable level of distortions in a tuned region of its
parameter space, namely the original hybrid model. Three effective multi-field
scenarios are also studied: with softly and suddenly turning trajectories, and
with a mild waterfall trajectory. Softly turning trajectories do not induce
distortions at any detectable level, whereas a sudden turn in the field space
or a mild waterfall trajectory predicts a peak (plus damped oscillations in the
sudden turn case) in the scalar power spectrum, which can lead to an observable
amount of CMB distortions. Finally, another scenario leading to potentially
detectable distortions involves a curvaton whose blue spectrum is subdominant
on CMB angular scales and overtakes the inflaton spectrum on smaller scales. In
this case however, we show that the bounds from ultra compact minihaloes are
not satisfied. Expectations for an ultimate PRISM-class experiment
characterized by an improvement in sensitivity by a factor of ten are discussed
for some models.
