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 fluctuation 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.