  We study the impact of (generalized) cuscuton models on standard single
scalar field inflation. Generalized cuscuton models are characterized by
spatial covariant gravity where a scalar degree of freedom is made non
dynamical, and there are just two tensor degrees of freedom. The presence of
the non-dynamical scalar field does not spoil inflation but instead the
modifications are, in general, slow-roll suppressed leading to almost
scale-invariant power spectra. However, the extra free parameters, which can be
tuned relatively independently, lead to a larger parameter range for observable
quantities, such as the tensor-to-scalar ratio. For the (generalized) cuscuton
model the non-Gaussianties of the curvature bispectrum are suppressed by the
slow-roll parameters, and, therefore, outside the reach of current experiments.
However, generalized cuscuton models can lead to a different shape for the
bispectrum which might be constrained by future experiments.
