  We compute corrections to the inflationary potential due to conformally
coupled non-relativistic matter. We find that under certain conditions of the
matter coupling, inflation may be interrupted abruptly. We display this in the
superconformal Starobinsky model, where matter is conformally coupled to the
Einstein frame metric. These corrections may easily stop inflation provided
that there is an initial density of non-relativistic matter. Since these
additional heavy degrees of freedom generically occur in higher dimension
theories, for example as Kaluza-Klein modes, this effect can arise in multiple
scenarios.
