Einstein Gravity from Conformal Gravity

Understand

We show that that four dimensional conformal gravity plus a simple Neumann boundary condition can be used to get the semiclassical (or tree level) wavefunction of the universe of four dimensional asymptotically de-Sitter or Euclidean anti-de Sitter spacetimes.

• This simple Neumann boundary condition selects the Einstein solution out of the more numerous solutions of conformal gravity.
• It thus removes the ghosts of conformal gravity from this computation.
• In the case of a five dimensional pure gravity theory with a positive cosmological constant we show that the late time superhorizon tree level probability measure, $|\Psi [ g ]|^2$, for its four dimensional spatial slices is given by the action of Euclidean four dimensional conformal gravity.