$\lambda \phi^4$ in de Sitter

by Leonardo Senatore (Stanford University)

Friday 25 May 2018, 14:30 → 15:30 Europe/Zurich

4/3-006 - TH Conference Room (CERN)

Correlation functions in massless $\lambda \phi^4$ in de Sitter space are IR divergent, indicating that the interacting vacuum of the theory is non-perturbatively far from the free vacuum. This gives rise to worries that de Sitter space might actually be unstable. We introduce two different perturbative schemes for sub-horizon and super-horizon modes. While short modes are solved for with the familiar expansion in powers of the coupling constant $\lambda$, the long modes are perturbatively solved for by expanding in $\hbar$, gradients and square-root of $\lambda$. At leading order in all these parameters, the density matrix for the long modes satisfies a Fokker-Planck equation, as envisioned long-time ago by Starobinsky. A generalized equation allows us to compute the corrections in all the expansion parameters. We compute explicitly the ones in square-root of $\lambda$, which are the leading ones. Our results provide not only a solution to the problem of $\lambda \phi^4$ in de Sitter space, but also offer a rigorous proof of the existence of slow-roll eternal inflation.