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Abstract We re-consider the graviton self-energy induced by a loop of massless, minimally coupled scalars on de Sitter background. On flat space background it can be represented as a sum of two tensor differential operators acting on scalar structure functions. On a general background these differential operators can be constructed from the linearized Ricci scalar and the linearized Weyl tensor. However, in cosmology one requires a third contribution which we derive here. 

Abstract In the peculiar manner by which physicists reckon descent, this article is by a ‘child’ and ‘grandchild’ of the late Stanley Deser. We begin by sharing reminiscences of Stanley from over 40 years. Then we turn to a problem which was dear to his heart: the prospect that gravity might nonperturbatively screen its own ultraviolet divergences and those of other theories. After reviewing the original 1960 work by ADM, we describe a cosmological analogue of the problem and then begin the process of implementing it in gravity plus QED. 

Abstract We consider the classic question posed by Pardo and Spergel about theprice of abandoning dark matter in the context of an invariant,metric-based theory of gravity. Our answer is that the price isnonlocality. This has been known for some time in the context of thequasi-static regime. We show that it also applies for cosmology andwe exhibit a model which reproduces standard CDM successes such asperturbations in the cosmic microwave background, baryon acousticoscillations and structure formation. 

A<sc>bstract</sc> Dependence on the graviton gauge enters the conventional effective field equations because they fail to account for quantum gravitational correlations with the source which excites the effective field and with the observer who measures it. Including these correlations has been shown to eliminate gauge dependence in flat space background. We generalize the technique to de Sitter background for the case of the 1-loop graviton corrections to the exchange potential of a massless, minimally coupled scalar. 

A<sc>bstract</sc> Recent progress on nonlinear sigma models on de Sitter background has permitted the resummation of large inflationary logarithms by combining a variant of Starobinsky’s stochastic formalism with a variant of the renormalization group. We reconsider single graviton loop corrections to the photon wave function, and to the Coulomb potential, in light of these developments. Neither of the two 1-loop results have a stochastic explanation, however, the flow of a curvature-dependent field strength renormalization explains their factors of ln(a). We speculate that the factor of ln(Hr) in the Coulomb potential should not be considered as a leading logarithm effect. 

A<sc>bstract</sc> Nonlinear sigma models on de Sitter background have proved a useful prototype for quantum gravity in summing the large logarithms which arise from loop corrections. We consider a model whose evolution is described, at leading logarithm order, by the trace of the coincident, doubly differentiated scalar propagator. An analytic approximation for this quantity on an arbitrary expansion history is applied to generalize the resummed de Sitter result to any cosmological background which has experienced primordial inflation. In addition to analytic expressions, we present explicit numerical results for the evolution in a plausible expansion history. The large scales of primordial inflation are transmitted to late times. 

The continual production of gravitons during inflation endows loop corrections with secular logarithms which grow nonperturbatively large during a prolonged period of inflation. The physics behind these effects is reviewed, along with a catalog of the examples which have so far been found. Resummation can be accomplished by combining a variant of Starobinsky’s stochastic formalism with a variant of the renormalization group. The issue of gauge independence is also addressed. 

The continual production of long wavelength gravitons during primordial inflation endows graviton loop corrections with secular growth factors. During a prolonged period of inflation, these factors eventually overwhelm the small loop-counting parameter of GH2, causing perturbation theory to break down. A technique was recently developed for summing the leading secular effects at each order in non-linear sigma models, which possess the same kind of derivative interactions as gravity. This technique combines a variant of Starobinsky’s stochastic formalism with a variant of the renormalization group. Generalizing the technique to quantum gravity is a two-step process, the first of which is the determination of the gauge fixing condition that will allow this summation to be realized; this is the subject of this paper. Moreover, we briefly discuss the second step, which shall obtain the Langevin equation, in which secular changes in gravitational phenomena are driven by stochastic fluctuations of the graviton field.