1. Toward a theory of de Sitter space? Donald Marolf May 25, 2007 Based on work w/Steve Giddings.

2. Results dS: A laboratory to study locality (& more?) in perturbative gravity dS: A laboratory to study locality (& more?) in perturbative gravity Constraints  each state dS invariant Constraints  each state dS invariant Finite # of pert states for eternal dS (pert. theory valid everywhere) Limit ``energy’’ of seed states to avoid strong gravity. (Any Frame) Compact & finite F  finite N. S = ln N ~ ( l/l p ) (d-2)(d-1)/d < S dS Finite # of pert states for eternal dS (pert. theory valid everywhere) Limit ``energy’’ of seed states to avoid strong gravity. (Any Frame) Compact & finite F  finite N. S = ln N ~ ( l/l p ) (d-2)(d-1)/d < S dS neck Consider F = q T ab n a n b

3. Observables? Try O = -g A(x) x dS Finite ( H 0 ) matrix elements for appropriate A(x), |  i >. Also dS-invariant to preserve H phys. A composite, VeV of A =0

4. Relational observables recover local physics let O = -g A(x), x dS A(x) =  (x)   (x)   (x) Given scalars  , , I.e., O scans spacetime for intersection (“observer”), reports value of . If |  > has 1  -particle and 1  -particle,, then ~ If |  > has 1  -particle and 1  -particle,, then ~   Proto-local?

5. But fluctuations diverge! Work with seed states; Recall |0> is an attractor…. = dx 1 dx 2 = dx 1 dx 2 ~ dx 1 dx 2 ~ dx 1 dx 2 ~ const(V dS ) Note: =  i. control intermediate states? O = P O P for P a finite-dim projection; e.g. F < f. dS UV/IR: Use “Energy” cut-off to control spacetime volume O is insensitive to details of long time dynamics, as desired. Choose f to control “noise;” safe for f ~ M maxBH. Heavy reference object (“observer”)  safe for f ~ exp(S dS ), V < l (d-1) S dS ~ (vacuum noise, BBs) ~ O Proto-local ~

6. Fundamental Lessons for cosmology? No fundamental ``classical observers.” Study quantum observers & observables. Study fluctuations. No fundamental ``classical observers.” Study quantum observers & observables. Study fluctuations. Locality is approximate; no absolute Hamiltonian (no surprise, but no ``hot box’’) Locality is approximate; no absolute Hamiltonian (no surprise, but no ``hot box’’) Approx. local physics over V < exp(S dS ) (smaller for light observer/observable) For larger V, “BB”-like vacuum noise dominates Approx. local physics over V < exp(S dS ) (smaller for light observer/observable) For larger V, “BB”-like vacuum noise dominates Quantum observers/observables are global constructions. Quantum observers/observables are global constructions. Finite S for eternal dS, but naturally embeds in larger infinite-dimensional theories.  Similar results for eternal inflation, etc. ?? Finite S for eternal dS, but naturally embeds in larger infinite-dimensional theories.  Similar results for eternal inflation, etc. ??