**3.3. Gaussianity and adiabaticity**

While the simplest models of inflation predict gaussian adiabatic perturbations, many models are known which violate either or both of these conditions. Consequently there is no critical test of inflation which can be simply stated. Nevertheless, it is clear that these could lead to tests of the inflationary paradigm. For example, as far as inflation is concerned, there is good nongaussianity and bad nongaussianity. For example, if line discontinuities are seen in the microwave background, it would be futile to try and explain them using inflation rather than cosmic strings. On the other hand, nongaussianity with a chi-squared distribution is very easy to generate in inflation models; one only has to arrange that the leading contribution to the density comes from the square of a scalar field perturbation. Indeed, in isocurvature inflation models, it appears at least as easy to arrange chi-squared statistics as it is to arrange gaussian ones [19].

Inflation may also be able to explain nongaussian perturbations of a `bubbly' nature, by attributing the bubbles to a phase transition bringing inflation to an end. The simplest models of this type have already been excluded, but more complicated ones may still be viable.