|Speaker:||Richard Holman (Carnegie Mellon University)|
|Title:||EFT Beyond the Horizon: Stochastic Inflation and How Primordial Quantum Fluctuations Go Classical|
|Date (JST):||Fri, Sep 26, 2014, 13:30 - 14:30|
|Place:||Seminar Room A|
We identify the effective field theory describing the physics of super-Hubble scales and show it to be a special case of a class of effective field theories appropriate to open systems,i.e. those that allow information to be exchanged between the degrees of freedom of interest and those that are integrated out. Strictly speaking they cannot in general be described
by an effective lagrangian; rather the appropriate `low energy' limit is instead a Lindblad equation describing the time-evolution of the density matrix of the slow degrees of freedom. We derive the equation relevant to super-Hubble modes of quantum fields in de Sitter (and near-de Sitter) spacetimes and derive two of its implications. We show that the evolution of the diagonal density-matrix elements quickly approach the Fokker-Planck equation of Starobinsky's stochastic inflationary picture. This allows us both to identify the leading corrections and provide an alternative first-principles derivation of this picture's stochastic noise and drift. We then argue that the presence of interactions drive the off-diagonal density-matrix elements to zero in the field basis. This shows why the field basis is generally the
`pointer basis' for the process that decoheres primordial quantum fluctuations while they are outside the horizon, thus allowing them to re-enter later as classical field fluctuations, as assumed when analyzing CMB data. The decoherence process is very efficient, occurring after several Hubble times even for interactions as weak as gravitational-strength. Crucially, the details of the interactions largely control only the decoherence time and not the nature of the final late-time stochastic state, much as interactions can control the equilibration time for thermal systems but are largely irrelevant to the properties of the resulting equilibrium state.