Exact solution to perturbative conformal cosmology in the recombination
  era
  We study cosmological perturbation theory in the cosmology associated with
conformal gravity, establish the validity of the decomposition theorem for it,
and then use the theorem to provide an exact solution to the theory in the
recombination era. Central to our approach is the use of a fully gauge
invariant formulation of the cosmological fluctuations equations. In the
recombination era not only is perturbation theory applicable, because of its
specific structure in the conformal case the fluctuation equations are found to
greatly simplify. Using a master equation for scalar, vector and tensor
fluctuation modes we show that the radial equations for the three-dimensional
vector and tensor modes are respectively the same as those of scalar modes in
five and seven spatial dimensions. This enables us to construct normalization
conditions for the three-dimensional modes.
