  We present the first steps needed for an analysis of the perturbations that
occur in the cosmology associated with the conformal gravity theory. We discuss
the implications of conformal invariance for perturbative coordinate gauge
choices, and show that in the conformal theory the trace of the metric
fluctuation kinematically decouples from the first-order gravitational
fluctuation equations. We determine the equations that describe first-order
metric fluctuations around the illustrative conformally flat de Sitter
background. Via a conformal transformation we show that such fluctuations can
be constructed from fluctuations around a flat background, even though the
fluctuations themselves are associated with a perturbative geometry that is not
itself conformal to flat. We extend the analysis to fluctuations around other
cosmologically relevant backgrounds, such as the conformally-flat
Robertson-Walker background, and find tensor fluctuations that grow far more
rapidly than those that occur in the analogous standard case. We comment on
some recent work by 't Hooft and by Maldacena on deriving conformal gravity
from Einstein gravity or vice versa. We show that while the standard gravity
tensor fluctuations around a de Sitter background are also fluctuation
solutions in the conformal theory, in the conformal case they do not carry
energy.
