Abstract
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.
Highlights
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
The point of this paper is to demonstrate that the large logarithmics of nonlinear sigma models on de Sitter can be explained by combining a variant of Starobinsky’s stochastic formalism with a variant of the renormalization group
We demonstrate that many of these large logarithms arise from stochastic effects associated with a curvature-dependent effective potential induced by the kinetic terms
Summary
This section introduces the two models upon which this study is based. The first is a single field model which gives a free theory by a local field redefinition; the second is a model based on two fields which is fundamentally interacting. For each model we give the bare Lagrangian and the first two variations of the action. We present the Feynman rules and some important identities for the coincidence limits of the propagator
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