Abstract
It is well-known that expectation values in de Sitter space are afflicted by infra-red divergences. Long ago, Starobinsky proposed that infra-red effects in de Sitter space could be accommodated by evolving the long-wavelength part of the field according to the classical equations of motion plus a stochastic source term. I argue that — when quantum-mechanical loop corrections are taken into account — the separate universe picture of superhorizon evolution in de Sitter space is equivalent, in a certain leading-logarithm approximation, to Starobinsky's stochastic approach. In particular the time evolution of a box of de Sitter space can be understood in exact analogy with the DGLAP evolution of partons within a hadron, which describes a slow logarithmic evolution in the distribution of the hadron's constituent partons with the energy scale at which they are probed.
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