Abstract

It is well known that expectation values of scalar field fluctuations in de Sitter space, such as those used to study the temperature anisotropy of the CMB , are afflicted with infra-red divergences. Long ago, Starobinsky proposed that some infra-red effects could be captured by coarse-graining over the long wavelength part of the fields, yielding a stochastic picture of spacetime on the very largest scales. I show that when quantum-mechanical loop corrections are taken into account the popular `separate universe’ picture of superhorizon evolution is exactly equivalent, in the leading logarithm approximation, to Starobinsky’s method. 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 of the hadron’s constituent partons with the energy scale at whichthey are probed.