  We investigate glueball inflation model-building via the methods of the
gauge/gravity duality. For that purpose, we consider a certain 5d consistent
truncation of type IIB supergravity. This theory admits a solution, whose
metric is of the form of a $dS_4$ fibration over a fifth dimension. We find a
new time-dependent deformation around this solution, which allows for a small
$\eta$ parameter of the corresponding inflationary model. This resolves a
problem with a previous solution that allowed only $\eta$ of order one and thus
gave only an ultra-slow roll regime, but not regular slow roll.
