Einstein Gravity from Conformal Gravity

TL;DR

This paper demonstrates that four-dimensional conformal gravity with a Neumann boundary condition can reproduce Einstein gravity solutions and eliminate ghosts, providing a new perspective on the wavefunction of the universe in de-Sitter and anti-de Sitter spacetimes.

Contribution

It introduces a boundary condition in conformal gravity that isolates Einstein solutions and removes ghost solutions, linking conformal gravity to Einstein gravity in a novel way.

Findings

Neumann boundary condition selects Einstein solutions

Conformal gravity reproduces Einstein wavefunction

Ghosts are removed in this formulation

Abstract

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.