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 $\ensuremath{\sigma}$ triggered by another scalar field $\ensuremath{\varphi}$. This model looks like a hybrid of chaotic inflation with $V(\ensuremath{\varphi})=\frac{{m}^{2}{\ensuremath{\varphi}}^{2}}{2}$ and the usual theory with spontaneous symmetry breaking with $V(\ensuremath{\sigma})=\frac{1}{4\ensuremath{\lambda}}{({M}^{2}\ensuremath{-}\ensuremath{\lambda}{\ensuremath{\sigma}}^{2})}^{2}$. The last stages of inflation in this model are supported not by the inflaton potential $V(\ensuremath{\varphi})$ but by the "noninflationary" potential $V(\ensuremath{\sigma})$. 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 $\ensuremath{\sigma}$). In the simplest version of this scenario inflation ends up by slow rolling, thus avoiding the big-bubble problem of extended inflation.