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arXiv · 2609.34788

The separate universe approach with non minimal coupling to gravity

Hugo Holland·Julien Grain
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Abstract

In this paper we extend a study of the validity conditions of the separate universe approach of cosmological perturbations to models of inflation with multiple fields that are non minimally coupled to gravity. The separate universe approach effectively describes the universe as a collection of homogeneous and isotropic patches, leading to an effective description of cosmological perturbations at large scales. This approximation is a necessary step in stochastic inflation and in the $δ\N$ formalism. We study and compare the dynamics of cosmological perturbation theory at large scales to the dynamics derived in the separate universe picture for non linear sigma models where we have allowed a non minimal coupling between the fields and gravity. We found that the separate universe approach adequately reproduces the dynamics of the large scale perturbations, provided the wavelength of the modes considered is greater than a list of lower bounds derived from the background evolution of the model we consider. These lower bounds are then compared to those derived in the classically equivalent Einstein frame description of the Jordan frame model at hand. In particular these conditions are derived and compared for a Higgs-like toy model of inflation in the large field limit.

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Hugo Holland, Julien Grain. 2026-09-28. The separate universe approach with non minimal coupling to gravity. https://arxiv.org/abs/2609.34788

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