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Understanding the origin of cosmic structure requires connecting quantum fluctuations in the early Universe to nonlinear dynamics that shape cosmological observables. While linear perturbation theory successfully describes the primordial fluctuations probed by CMB anisotropies, many key processes --- including preheating, gauge-field production, primordial-black-hole formation, and stochastic gravitational-wave generation --- are intrinsically nonlinear and require real-space numerical methods.
In this talk, I will present recent efforts to develop a framework and associated computational tool for nonlinear cosmology. I will first discuss post-inflationary gauge-field production, where resonance, backreaction, and dark-sector dynamics can generate stochastic gravitational waves. I will then describe a complementary framework for inflationary dynamics in which the local expansion history is evolved on the lattice through an inhomogeneous FLRW geometry. I will further explain how this framework provides an efficient bridge between conventional rigid-FLRW simulations and full numerical relativity, enabling studies of stochastic effects, nonlinear curvature perturbations, and primordial non-Gaussianity.
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