What differentiates inflationary models from each other?

[windy miller]

How do the different inflationary models different form each other. Is is just the shape of the potential or the number of fields assumed or...?

 

[Chalnoth]

Most inflation models are single-field. Multiple-field inflation models are relatively uncommon. So they mostly differ by the shape of the potential.

 

[bapowell]

How do the different inflationary models different form each other. Is is just the shape of the potential or the number of fields assumed or...?

You've also got gravitational couplings and the form of the kinetic energy term. The perturbations might further depend on the vacuum chosen and whether something other than the inflaton generated them (curvaton, modulated reheating).