Speaker
Description
The classical evolution of fields during a period of accelerated expansion in the very early universe ("inflation") can establish an idealised homogeneous and isotropic cosmology. However, quantum fluctuations inevitably generate inhomogeneities and anisotropies on all observable scales and beyond. The $\delta N$ formalism provides a powerful framework to describe the nonlinear curvature perturbation in terms of fluctuations in the duration of inflation, $N$. In its standard implementation, $\delta N$ is calculated using the classical trajectory to find the number of e-folds of inflation from a given field value to the end of inflation. In contrast, the stochastic $\delta N$ formalism incorporates quantum fluctuations as stochastic noise along the trajectory, enabling a non-perturbative treatment of inflationary dynamics that can be crucial for rare, large fluctuations. In this work, we compare the classical and stochastic approaches to study the statistics of large curvature perturbations when coarse-grained at a given length scale. This is particularly relevant for calculations of primordial black hole formation. Using the numerical code PyFPT, we compute the distribution of curvature perturbations from slow-roll inflation driven by a quadratic potential, and perform a detailed comparison with the classical $\delta N$ formalism, identifying regimes where quantum diffusion significantly impacts the probability distribution of large fluctuations.
| Other topic / keywords: | Primordial Black Holes, Stochastic Inflation |
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