Hybrid inflation

Usually inflation ends either by a slow rolling of the inflation field, which gradually becomes faster and faster, or by a first-order phase transition. We describe a model where inflation ends in a different way, due to a very rapid rolling ("waterfall") of a scalar field $\sigma$ triggered by another scalar field $\phi$. This model looks like a hybrid of chaotic inflation with $V\left(\phi \right)=\frac{m^2{\phi }^2}{2}$ and the usual theory with spontaneous symmetry breaking with $V\left(\sigma \right)=\frac{1}{4\lambda }{(M^2-\lambda {\sigma }^2)}^2$. The last stages of inflation in this model are supported not by the inflaton potential $V\left(\phi \right)$ but by the "noninflationary" potential $V\left(\sigma \right)$. Another hybrid model to be discussed here uses some building blocks from extended inflation (Brans-Dicke theory), from new inflation (phase transition due to a nonminimal coupling of the inflaton field to gravity), and from chaotic inflation (the possibility of inflation beginning at large as well as at small $\sigma$). In the simplest version of this scenario inflation ends up by slow rolling, thus avoiding the big-bubble problem of extended inflation.