Quantum Walks and RG in de Sitter Space

Classical random walks have long served as useful intuition for the dynamics of light scalar fields in de Sitter space. This description can be shown to arise from QFT on a fixed dS background, via RG flow. The RG approach also permits corrections to the stochastic formalism to be calculated systematically, but fails to describe the tails of the probability distribution. After reviewing these results, I will show how to improve these results using exact RG and the dS density matrix. We will find this gives rise to a quantum walk and will use this perspective to resolve some open issues with the stochastic formalism.