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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. 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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3. Unfinished business in a nonlinear sigma model on de Sitter background

   https://doi.org/10.1007/JHEP06(2023)206  

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

   A bstract Nonlinear sigma models on de Sitter background possess the same kind of derivative interactions as gravity, and show the same sorts of large spacetime logarithms in correlation functions and solutions to the effective field equations. It was recently demonstrated that these logarithms can be resummed by combining a variant of Starobinsky’s stochastic formalism with a variant of the renormalization group. This work considers one of these models and completes two pieces of analysis which were left unfinished: the evolution of the background at two loop order and the one loop beta function. 

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4. Universality of loop corrected soft theorems in 4d

   https://doi.org/10.1007/JHEP11(2023)233  

   Krishna, Hare; Sahoo, Biswajit (November 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> In [1], logarithmic correction to subleading soft photon and soft graviton theorems have been derived in four spacetime dimensions from the ratio of IR-finite S-matrices. This has been achieved after factoring out IR-divergent components from the traditional electromagnetic and gravitational S-matrices using Grammer-Yennie prescription. Although the loop corrected subleading soft theorems are derived from one-loop scattering amplitudes involving scalar particles in a minimally coupled theory with scalar contact interaction, it has been conjectured that the soft factors are universal (theory independent) and one-loop exact (don’t receive corrections from higher loops). This paper extends the analysis conducted in [1] to encompass general spinning particle scattering with non-minimal couplings permitted by gauge invariance and general coordinate invariance. By re-deriving the lnωsoft factors in this generic setup, we establish their universal nature. Furthermore, we summarize the results of loop corrected soft photon and graviton theorems up to sub-subleading order, which follows from the analysis of one and two loop QED and quantum gravity S-matrices. While the classical versions of these soft factors have already been derived in the literature, we put forth conjectures regarding the quantum soft factors and outline potential strategies for their derivation. 

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5. Leading Logarithm Quantum Gravity

   https://doi.org/10.3390/universe11070223  

   Miao, S P; Tsamis, N C; Woodard, R P (July 2025, Universe)

   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. 

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