  We investigate density perturbations generated through modulated reheating
while inflation is driven by a conformally coupled scalar field. A large
running of the spectral index is obtained, which reflects the basic nature of
conformal inflation that higher-order time derivatives of the Hubble parameter
during inflation are not necessarily small. This feature may allow us to
distinguish between conformal inflation models and standard minimally coupled
ones. We also investigate how the resulting fluctuations are modified when
there is a deviation from an exact conformal coupling between the inflaton and
gravity. Finally, we apply our results to the warped brane inflation model and
see that observational bounds from the WMAP5 data suggest a blue tilted density
perturbation spectrum.
