Joint cosmology seminar at MIT:

Wednesday, November 27, 2019, 2:30 pm
Cosman Seminar Room
Center for Theoretical Physics
Building 6C, Room 6C-442
Massachusetts Institute of Technology
Refreshments at 2:00 in the same room

$\lambda \phi^4$ in de Sitter

Leonardo Senatore
Stanford

Abstract:

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 obtain the corrections in all the expansion parameters. We compute explicitly the ones in square-root of $\lambda,$ which are the leading ones. We provide several checks, such as the fact that, on the static patch, correlation functions are thermal. 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.