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1. Summing inflationary logarithms in nonlinear sigma models

   https://doi.org/10.1007/JHEP03(2022)069  

   Miao, S. P.; Tsamis, N. C.; Woodard, R. P. (March 2022, Journal of High Energy Physics)

   A bstract We consider two nonlinear sigma models on de Sitter background which involve the same derivative interactions as quantum gravity but without the gauge issue. The first model contains only a single field, which can be reduced to a free theory by a local field redefinition; the second contains two fields and cannot be so reduced. Loop corrections in both models produce large temporal and spatial logarithms which cause perturbation theory to break down at late times and large distances. Many of these logarithms derive from the “tail” part of the propagator and can be summed using a variant of Starobinsky’s stochastic formalism involving a curvature-dependent effective potential. The remaining logarithms derive from the ultraviolet and can be summed using a variant of the renormalization group based on a special class of curvature-dependent renormalizations. Explicit results are derived at 1-loop and 2-loop orders. 

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2. Explaining large electromagnetic logarithms from loops of inflationary gravitons

   https://doi.org/10.1007/JHEP08(2023)195  

   Glavan, D; Miao, S P; Prokopec, T; Woodard, RP (August 2023, Journal of High Energy Physics)

   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. 

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3. How Inflationary Gravitons Affect the Force of Gravity

   https://doi.org/10.3390/universe8070376  

   Tan, Lintao; Tsamis, Nikolaos Christos; Woodard, Richard Paul (July 2022, Universe)

   We employ an unregulated computation of the graviton self-energy from gravitons on the de Sitter background to infer the renormalized result. This is used to quantum-correct the linearized Einstein equation. We solve this equation for the potentials that represent the gravitational response to a static, point mass. We find large spatial and temporal logarithmic corrections to the Newtonian potential and to the gravitational shift. Although suppressed by a minuscule loop-counting parameter, these corrections cause perturbation theory to break down at large distances and late times. Another interesting fact is that gravitons induce up to three large logarithms, whereas a loop of massless, minimally coupled scalars produces only a single large logarithm. This is in line with corrections to the graviton mode function: a loop of gravitons induces two large logarithms, whereas a scalar loop gives none. 

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4. Resummations for inflationary quantum gravity

   https://doi.org/10.1142/S0218271825420027  

   Woodard, R P (July 2025, International Journal of Modern Physics D)

   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. 

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5. Remembrance of things past

   https://doi.org/10.1007/JHEP08(2023)124  

   Woodard, R P; Yesilyurt, B (August 2023, Journal of High Energy Physics)

   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. 

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