A parton picture of de Sitter space during slow-roll inflation

TL;DR

This paper demonstrates that the superhorizon evolution in de Sitter space during slow-roll inflation can be understood as a parton-like evolution, linking quantum field theory in curved spacetime with parton distribution dynamics.

Contribution

It establishes an equivalence between the stochastic approach to de Sitter space and the parton evolution picture, incorporating quantum loop corrections in a leading-logarithm approximation.

Findings

Superhorizon evolution in de Sitter space is analogous to parton evolution in hadrons.

Quantum loop corrections support the stochastic description of long-wavelength modes.

The evolution follows a DGLAP-like logarithmic pattern.

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 field equations 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.