Quantum correlations for the metric

Understand

We discuss the correlation function for the metric for homogeneous and isotropic cosmologies.

• The exact propagator equation determines the correlation function as the inverse of the second functional derivative of the quantum effective action.
• This formulation relates the metric correlation function employed in quantum gravity computations to cosmological observables as the graviton power spectrum.
• In the Einstein-Hilbert approximation for the effective action the on-shell graviton correlation function can be obtained equivalently from a product of mode functions which solve the linearized Einstein equations.