Title: A Tail of Eternal Inflation

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Abstract:
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Recent developments in our understanding of quantum field theory in de Sitter space have revealed how to derive the equations Stochastic Inflation and included corrections to them systematically. In this talk, I will review the Soft de Sitter Effective Theory and how it enables to calculate these equations. I will then apply the results to massless $\lambda \phi^4$ theory in de Sitter and calculate the next-to-next-to leading order corrections to the equations and relaxation eigenvalues. We will then apply the same techniques to primordial non-Gaussianity in single-field inflation where we will find the onset of eternal inflation becomes incalculable in some surprising circumstances.