http://arxiv.org/abs/1603.06504
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, for which we take the Einstein-Hilbert approximation. This formulation relates the metric correlation function employed in quantum gravity computations to cosmological observables as the graviton power spectrum. While the graviton correlation function can be obtained equivalently as a solution of the linearized Einstein equations, this does not hold for the vector and scalar components of the metric. We project the metric fluctuations on the subspace of “physical fluctuations”, which couple to a conserved energy momentum tensor. On the subspace of physical metric fluctuations the relation to physical sources becomes invertible, such that the effective action and its relation to correlation functions does not need gauge fixing. The physical metric fluctuations have a similar status as the Bardeen potentials, while being formulated in a covariant way. We compute the effective action for the physical metric fluctuations for geometries corresponding to realistic cosmologies.
C. Wetterich
Tue, 22 Mar 16
54/72
Comments: 36 pages
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