Stochastic dynamics of cosmological inflation in general relativity

Abstract

The theory of Inflation, supplemented by fluctuations of the quantum vacuum, is the leading paradigm to explain the correlations of inhomogeneities at very large distances in the Universe. Particle physics methods fail when strong non-linearity and non-perturbativity are involved, leaving a whole landscape of untestable scenarios of inflation. Starobinsky's stochastic inflation can in principle treat inflationary inhomogeneities nonlinearly and classically as the Hubble radius becomes smaller than their wavelengths, but it was never formulated in full general relativity, which motivates this thesis. Using the Keldysh formalism of nonequilibrium quantum field theory, we first develop a validity criterion for the use of classical computations, and thus simulations, to probe inflationary interactions, finding analytically that the bispectrum can be extracted from slightly sub-Hubble scales in quasi-de Sitter spacetimes. We then provide the first analytical solutions to the constraints for inhomogeneous initial conditions of numerical relativity simulations of inflation, and use them to explore its nonperturbative regime. Our main contribution is to obtain stochastic equations for the full set of inflaton equations in general relativity: this description incorporates the full nonlinear and backreacting evolution, is small-gauge-invariant, and is free of historical assumptions such as the gradient-free separate universe approximation. We implement these equations in the BSSN formulation of numerical relativity, demonstrating their correctness in slow-roll and ultra slow-roll scenarios via the satisfaction of the constraints, with a first look at eternal inflation. Finally, we extend our coarse-graining methods beyond General Relativity and single-field inflation, offering a phenomenological framework with the ambition of serving as a numerical particle collider for the early universe.