  We summarize our work on building glueball inflation models with the methods
of the gauge/gravity duality. We review the relevant five-dimensional
consistent truncation of type IIB supergravity. We consider solutions of this
effective theory, whose metric has the form of a $dS_4$ foliation over a radial
direction. By turning on small (in an appropriate sense) time-dependent
deformations around these solutions, one can build models of glueball
inflation. We discuss a particular deformed solution, describing an ultra-slow
roll inflationary regime.
