Toward a theory of de Sitter space?

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Toward a theory of de Sitter space?

• Donald Marolf
• May 25, 2007

Based on work w/Steve Giddings.
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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 lt SdS

Consider F q Tab nanb
neck
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Observables?
Also dS-invariant to preserve Hphys.
Try O -g A(x)
A composite, VeV of A 0
Finite (H0) matrix elements lty1Oy2gt for
appropriate A(x), yigt.
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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 ygt has 1 b-particle and 1 g-particle,, then
ltYOYgt ltyf(x)ygt
I.e., O scans spacetime for intersection
(observer),reports value of f.
Proto-local?
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But fluctuations diverge!

• Work with seed states
• Recall 0gt is an attractor.

lty1O1O2y2gt dx1 dx2 lty1A1(x1)A2(x2)y2gt
dx1 dx2
lt0A1(x1)A2(x2)0gt
const(VdS)
(vacuum noise, BBs)
Note lty1O1O2y2gt Si lty1O1igtltiO2y2gt .
control intermediate states? O P O P for P
a finite-dim projection e.g. F lt 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 lt
l(d-1) SdS



O Proto-local
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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 lt 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. ??