Exact solution to perturbative conformal cosmology in the recombination era

TL;DR

This paper provides an exact, gauge-invariant solution to cosmological perturbations during the recombination era within conformal gravity, revealing simplified fluctuation equations and novel mode normalization conditions.

Contribution

It introduces an exact solution framework for perturbations in conformal gravity during recombination, utilizing a gauge-invariant approach and revealing dimensional analogies for fluctuation modes.

Findings

Perturbation equations simplify significantly in conformal gravity during recombination.

Radial equations for vector and tensor modes match those of scalar modes in higher dimensions.

Normalization conditions for fluctuation modes are established based on these equations.

Abstract

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.