Title: Power spectrum in stochastic inflation

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Abstract:
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The stochastic formalism of inflation can describe long-wavelength perturbations nonperturbatively. In this picture, inflaton fields coarse-grained over superhorizon scales evolve with random noises. Hence, the local duration of inflation becomes a random variable called the first-passage time, which is determined by the stochastic process. Fluctuations of the first-passage time are nothing but adiabatic curvature perturbations. This methodology to study curvature perturbations is called the stochastic-\delta N formalism. The preceding works have established methods to investigate statistics of the first-passage time starting from a fixed field value. However, to make concrete contact with observations, we rather need to know curvature perturbations associated with a certain scale. In this work, we compute the power spectrum of curvature perturbations in the stochastic-\delta N formalism taking into account the deviation from the classical relation between scales and field values. After showing our formalism, I will also talk about an application, where we find that quantum diffusion near the end of inflation can affect large-scale perturbations significantly. This indicates that the cosmic microwave background measurements can set explicit constraints on the entire inflationary potential. The talk will be based on the following paper:

https://arxiv.org/abs/2012.02031