  In low scale quantum gravity scenarios the fundamental scale of nature can be
as low as TeV, in order to address the naturalness of the electroweak scale. A
number of difficulties arise in constructing specific models; stabilisation of
the radius of the extra dimensions, avoidance of overproduction of Kaluza Klein
modes, achieving successful baryogenesis and production of a close to
scale-invariant spectrum of density perturbations with the correct amplitude.
We examine in detail the dynamics, including radion stabilisation, of a hybrid
inflation model that has been proposed in order to address these difficulties,
where the inflaton is a gauge singlet residing in the bulk. We find that for a
low fundamental scale the phase transition, which in standard four dimensional
hybrid models usually ends inflation, is slow and there is second phase of
inflation lasting for a large number of e-foldings. The density perturbations
on cosmologically interesting scales exit the Hubble radius during this second
phase of inflation, and we find that their amplitude is far smaller than is
required. We find that the duration of the second phase of inflation can be
short, so that cosmologically interesting scales exit the Hubble radius prior
to the phase transition, and the density perturbations have the correct
amplitude, only if the fundamental scale takes an intermediate value. Finally
we comment briefly on the implications of an intermediate fundamental scale for
the production of primordial black holes and baryogenesis.
