Cosmological Perturbations in Conformal Gravity

Understand

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.