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Toward a theory of de Sitter space?

Toward a theory of de Sitter space?. Donald Marolf May 25, 2007. Based on work w/Steve Giddings. Results. dS: A laboratory to study locality (& more?) in perturbative gravity Constraints  each state dS invariant

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Toward a theory of de Sitter space?

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  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 • 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/lp)(d-2)(d-1)/d < SdS Consider F = q Tab nanb neck

  3. x dS Observables? Also dS-invariant to preserve Hphys. Try O = -g A(x) A composite, VeV of A =0 Finite (H0) matrix elements <y1|O|y2> for appropriate A(x), |yi>.

  4. x dS Relational observablesrecover local physics Given scalars f,b, g, A(x) =f(x) b2(x) g2(x) b g let O = -g A(x), If |y> has 1 b-particle and 1 g-particle,,then <Y|O|Y> ~ <y|f(x)|y> I.e., O scans spacetime for intersection (“observer”),reports value of f. Proto-local?

  5. But fluctuations diverge! Work with seed states; Recall |0> is an attractor…. <y1|O1O2|y2> = dx1 dx2 <y1|A1(x1)A2(x2)|y2> ~ dx1 dx2 <0|A1(x1)A2(x2)|0> ~ const(VdS) (vacuum noise, BBs) Note: <y1|O1O2|y2> = Si <y1|O1|i><i|O2|y2> . 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 ~ MmaxBH. Heavy reference object (“observer”)  safe for f ~ exp(SdS), V < l(d-1) SdS ~ ~ ~ O Proto-local

  6. Fundamental Lessons for cosmology? • No fundamental ``classical observers.” Study quantum observers & observables. Study fluctuations. • Locality is approximate; no absolute Hamiltonian(no surprise, but no ``hot box’’) • Approx. local physics over V < exp(SdS) (smaller for light observer/observable)For larger V, “BB”-like vacuum noise dominates • 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. ??

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