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Bunch-Davies initial conditions and nonperturbative inflationary dynamics in numerical relativity

Yoann L. Launay1,*, Gerasimos I. Rigopoulos2,†, and E. Paul S. Shellard1,‡

  • *Contact author: yoann.launay@outlook.com
  • †Contact author: gerasimos.rigopoulos@ncl.ac.uk
  • ‡Contact author: eps1@cam.ac.uk
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Phys. Rev. D 112, 043518 – Published 15 August, 2025

DOI: https://doi.org/10.1103/qg66-gxh2

Abstract

We show that it is possible to simulate realistic inhomogeneities during cosmological inflation with high precision using numerical relativity. Stochastic initial conditions are set in line with the Bunch-Davies vacuum and satisfy the Hamiltonian and Momentum constraints of general relativity to leading order in perturbation theory. The subsequent fully nonlinear dynamical evolution is formulated within a family of geodesic gauges but can, in principle, be adapted to any choice of coordinates. We present three examples of inflationary dynamics: a simple quadratic potential, a potential with an inflection point, and a strong resonance model. When perturbations are small, we recover standard predictions of cosmological perturbation theory, and we quantify strongly nonlinear inhomogeneities when nonperturbative configurations emerge, such as in the strong resonance model. Our results pave the way toward the first realistic nonperturbative and fully nonlinear numerical relativity simulations of the early inflationary universe.

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Phys. Rev. D 112, 043518– Published 15 August, 2025
  • Received 12 March 2025
  • Accepted 23 July 2025
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