A shear-free lattice method bridges stochastic inflation and δN formalism by enabling fully nonlinear calculations of curvature perturbations in single-field models with ultra-slow-roll phases.
The influence of cosmological transitions on the evolution of density perturbations
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abstract
We study the influence of the reheating and equality transitions on superhorizon density perturbations and gravitational waves. Recent criticisms of the `standard result' for large-scale perturbations in inflationary cosmology are rectified. The claim that the `conservation law' for the amplitude of superhorizon modes was empty is shown to be wrong. For sharp transitions, i.e. the pressure jumps, we rederive the Deruelle-Mukhanov junction conditions. For a smooth transition we correct a result obtained by Grishchuk recently. We show that the junction conditions are not crucial, because the pressure is continuous during the reheating transition. The problem occurred, because the perturbed metric was not evolved correctly through the smooth reheating transition. Finally, we derive the `standard result' within Grishchuks's smooth (reheating) transition.
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Nonlinear Lattice Framework for Inflation: Bridging stochastic inflation and the $\delta{N}$ formalism
A shear-free lattice method bridges stochastic inflation and δN formalism by enabling fully nonlinear calculations of curvature perturbations in single-field models with ultra-slow-roll phases.