Nonlocal models of cosmology might derive from graviton loop corrections to the effective field equations from the epoch of primordial inflation. Although the Schwinger-Keldysh formalism would automatically produce causal and conserved effective fiel
d equations, the models so far proposed have been purely phenomenological. Two techniques have been employed to generate causal and conserved field equations: either varying an invariant nonlocal effective action and then enforcing causality by the ad hoc replacement of any advanced Greens function with its retarded counterpart, or else introducing causal nonlocality into a general ansatz for the field equations and then enforcing conservation. We point out here that the two techniques access very different classes of models, and that neither one of them may represent what would actually arise from fundamental theory.
After discussing the various issues regarding and requirements on pure quantum gravitational observables in homogeneous-isotropic conditions, we construct a composite operator observable satisfying most of them. We also expand it to first order in th
e loop counting parameter and suggest it as a physical quantifier of gravitational back-reaction in an initially inflating cosmology.
We compute the linearized Weyl-Weyl correlator using a new solution for the graviton propagator on de Sitter background in de Donder gauge. The result agrees exactly with a previous computation in a noncovariant gauge. We also use dimensional regular
ization to compute the one loop expectation value of the square of the Weyl tensor.
We reply to the recent criticism by Garriga and Tanaka of our proposal that quantum gravitational loop corrections may lead to a secular screening of the effective cosmological constant. Their argument rests upon a renormalization scheme in which the
composite operator $(R sqrt{-g} - 4 Lambda sqrt{-g} )_{rm ren}$ is defined to be the trace of the renormalized field equations. Although this is a peculiar prescription, we show that it {it does not preclude secular screening}. Moreover, we show that a constant Ricci scalar {it does not even classically} imply a constant expansion rate. Other important points are: (1) the quantity $R_{rm ren}$ of Garriga and Tanaka is neither a properly defined composite operator, nor is it constant; (2) gauge dependence does not render a Greens function devoid of physical content; (3) scalar models on a non-dynamical de Sitter background (for which there is no gauge issue) can induce arbitrarily large secular contributions to the stress tensor; (4) the same secular corrections appear in observable quantities in quantum gravity; and (5) the prospects seem good for deriving a simple stochastic formulation of quantum gravity in which the leading secular effects can be summed and for which the expectation values of even complicated, gauge invariant operators can be computed at leading order.
