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arXiv · 2502.06783

Bunch-Davies initial conditions and non-perturbative inflationary dynamics in Numerical Relativity

Yoann L. Launay·Gerasimos I. Rigopoulos·E. Paul S. Shellard
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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 non-linear dynamical evolution is formulated within a family of geodesic gauges but can in principle be adapted to any choice of coordinates. We present 3 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 non-linear inhomogeneities when non-perturbative configurations emerge, such as in the strong resonance model. Our results pave the way towards the first realistic non-perturbative, and fully non-linear Numerical Relativity simulations of the early inflationary universe.

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Yoann L. Launay, Gerasimos I. Rigopoulos, E. Paul S. Shellard. 2025-02-10. Bunch-Davies initial conditions and non-perturbative inflationary dynamics in Numerical Relativity. https://doi.org/10.1103/qg66-gxh2

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