Year: 2026
Type: preprint
Abstract: The theory of Inflation, supplemented by fluctuations of the quantum vacuum, is nowadays the leading and most general paradigm to explain the correlations of inhomogeneities at very large distances in the Universe. The study of the inflaton, and the prediction of its self-interactions in the expanding spacetime that it drives are key to constraining high-energy physics models for the origin of the Universe, including the unification of gravity and quantum mechanics. In the past decades, the application of particle physics methods to the cosmological context has provided perturbative predictions. However, whenever analyticity is lost or when strong non-linearity and non-perturbativity are involved, none of these tools, including semi-analytical methods, are sufficient to provide a complete picture of the underlying physics, leaving a whole landscape of untestable scenarios of inflation. An important advance in this respect has been A. Starobinsky’s stochastic inflation proposal, which can in principle treat nonlinearly and classically inflationary inhomogeneities as the Hubble radius becomes smaller than each of the wavelengths. However, this was never formulated in full general relativity, thus motivating the present work. After setting this broader context and using the Keldysh formalism of nonequilibrium quantum field theory, this thesis develops, in a first chapter, a validity criterion for the use of classical computations, and thus simulations, to probe inflationary interactions with correlation functions. In general relativity and standard quasi-De Sitter spacetimes, we find analytically that the bispectrum can be extracted from slightly sub-Hubble scales. This motivates the search for inhomogeneous initial conditions for numerical relativity simulations of inflation in the following chapter, providing the first analytical solutions to the constraints using standard cosmological perturbation theory. These are then used to explore the nonperturbative regime of inflationary dynamics in full numerical relativity, enabling so-called lattice cosmology to evolve the inflating spacetime fully. This formalism for initial conditions is later used for our main contribution: we show in another chapter how stochastic equations can be obtained for the complete set of equations of the inflaton in general relativity. In addition to incorporating the full nonlinear and backreacting evolution of inflation, this description is found to be gauge-invariant, and free of historical assumptions and associated caveats, such as the gradient-free separate universe approximation. We then present numerical implementations of these stochastic equations, cast in the BSSN formulation of numerical relativity, demonstrating their correctness in both a slow-roll and an ultra slow-roll scenario, particularly via the satisfaction of the constraints of general relativity. Our first preliminary demonstration within the wider inflationary landscape includes eternal inflation. In the final chapter, our coarse-graining methods prove to be robust and flexible enough to be extended beyond General Relativity and single-field inflation, offering a comprehensive phenomenological framework with the ambition of serving as a numerical particle collider for the early universe.
Source: arXiv (Cornell University)
DOI: 10.17863/cam.136383
Author: Launay, Yoann
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223681654