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Stochastic inflation beyond slow roll: noise modelling and importance sampling
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abstract
We simulate the distribution of very rare, large excursions in the primordial density field produced in models of inflation in the very early universe which include a strong enhancement of the power spectrum. The stochastic $\delta \mathcal{N}$ formalism is used to identify the probability distribution for the primordial curvature perturbation with the first-passage-time distribution, $P(\delta \mathcal{N})$, and we compare our stochastic results with those obtained in the classical $\delta \mathcal{N}$ approach. We extend the PyFPT numerical code to simulate the full 2D phase space, and apply importance sampling which allows very rare fluctuations to be simulated in $\mathcal{O}(10)$ minutes on a single CPU, where previous direct simulations required supercomputers. We demonstrate that the stochastic noise due to quantum fluctuations after a sudden transition to ultra-slow roll can be accurately modelled using an analytical Bessel-function ansatz to identify the homogeneous growing mode. The stochastic noise found in this way is a function of the field value only. This enables us to coarse grain the inflation field at the Hubble scale and include non-linear, stochastic evolution on all super-Hubble length scales.
Forward citations
Cited by 5 Pith papers
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Nonlinear Lattice Framework for Inflation: Bridging stochastic inflation and the $\delta{N}$ formalism
A shear-free locally FLRW lattice framework for single-field inflation captures spatially varying expansion, curvature corrections, and nonlinear δN observables at a fraction of the cost of full numerical relativity.
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How deep is the dip and how tall are the wiggles in inflationary power spectra?
In single-field PBH inflation models, a power-spectrum dip appears precisely when the inflaton velocity does not flip sign, and the peak amplitude scales as the inverse square of the dip amplitude.
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Harvesting primordial black holes from stochastic trees with $\texttt{FOREST}$
A stochastic-branching-tree implementation of inflation, FOREST, computes curvature maps and primordial black hole mass functions with cloud-in-cloud effects included.
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Deviations from Gaussian White Noise in Stochastic Inflation
Relaxing the sharp cutoff or the Bunch-Davies initial state in stochastic inflation makes the noise colored, and relaxing the initial state also makes it non-Gaussian.
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$\delta n$ formalism: A new formulation for the probability density of the curvature perturbation
A reformulation of the δN formalism that counts e-folds forward and exploits the superhorizon correlation between field and velocity to express the curvature perturbation PDF as a one-dimensional change of variables.
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