quantum cosmology · 2013. 9. 17. · quantum cosmology: prediction vs observation thomas hertog!!...
TRANSCRIPT
Quantum Cosmology: Prediction vs Observation
Thomas Hertog!
Institute for Theoretical Physics University of Leuven, Belgium!
COSMO2013, Cambridge
Why Quantum Cosmology?
� Observational signatures of Quantum Gravity!
� To predict a prior for (inflationary) cosmology!!
f
VHfLPREDICTING a PRIOR for Inflation!
f
VHfLPREDICTING a PRIOR for Inflation!
? ?
f
VHfLPREDICTING a PRIOR for Inflation!
Ψ è relative weighting è robust predictions
Outline
� Quantum Cosmology: Framework! � " è A prior for inflation!
� " è Anthropic selection !
� Holography: towards a precise form of " !
!
(g,φ) TIME
Classical Quantum
RADIUS
singular regular
No-Boundary Wave Function!Hartle, Hawking, 1983
No-Boundary Wave Function!
[
3g,�] ⇡ exp
��IE [
3g,�]/~�
(3g,�)
No-Boundary Wave Function!
REAL
COMPLEX
(3g,�)
[
3g,�] ⇡ exp
��IE [
3g,�]/~�= A exp(iS)
Emergent classical cosmology!
[
3g,�] ⇡ A exp(iS)
|rA| ⌧ |rS| Classical evolution!
MULTIVERSE pq = rqS
Phist / A2= exp(�2IR/~)
Inflation!
Inflation emerges as a prediction!
Hartle, Hawking, TH, 2008
h=mφ V (�) =
1
2m2�2
è Ψ implies vacuum selec-on
Probability distribution!
Slava’s talk
è Predictions for observations
| |2 / exp
✓⇡
4V (�0)
◆exp
⇣� ✏
H2n3⇣2n
⌘
Application: a Prior for Planck !
TH, 2013
Framework: 1. An unbiased landscape poten-al with a variety of single-‐field
infla-onary patches 2. The semiclassical no-‐boundary wave func-on
Ψ è relative weighting of landscape regions
Application: a Prior for Planck !
TH, 2013
PredicSons for ObservaSons: condi-onal probabili-es for observable features O given our observa-onal situa-on D
P (O|D) /X
J
ZP (O|�J
0 )P (D|O,�J0 )P (�J
0 )
Application: a Prior for Planck !
TH, 2013
PredicSons for ObservaSon: condi-onal probabili-es for observable features O given our observa-onal situa-on D
P (O|D) /X
J
ZP (O|�J
0 )P (D|O,�J0 )P (�J
0 )
“Anthropic” selection factor
No-boundary weighting
/ fgNHubble
fOc fEI fplf0
„3 pVEI
PHf0 DLfOc fEI
f
VHfL
V0(1� �n/µ+ · · · )��n
fOcfEIf
VHfL
fOcfEIf0
„3 pVEI
P Hf0 DL
Power law patches Plateau patches
8 HH
Planck 2013, XXII
Different regions in a single theory !
8 HH
tunneling
Assuming an unbiased landscape potential
Planck 2013, XXII
PredicSons for ObservaSon: condi-onal probabili-es for observable features O given our observa-onal situa-on D
P (O|D) /X
J
ZP (O|�J
0 )P (D|O,�J0 )P (�J
0 )
“Anthropic” selection factor
No-boundary weighting
/ fgNHubble
Anthropic Selection!Hartle, TH 13
Tegmark et al.06
Anthropic Selection!
P (⇤, Q|D) / fg(⇤, Q, t0)PNB(⇤, Q).
Weinberg Banks et al. Garriga, Vilenkin Tegmark et al. Livio, Rees
Flat Prior
PNB
Hartle, TH 2013
Open Questions
� Structure landscape potential � Formulation " beyond WKB limit!!� Unique " ?!
McAllister et al. Agarwal et al. Pedro, Westphal
Open Questions
� Structure landscape potential � Formulation " beyond WKB limit!!� Unique " ?!
McAllister et al. Agarwal et al. Pedro, Westphal
è holographic cosmology Maldacena Anninos et al. Castro, Maloney McFadden, Skenderis Hartle, Hawking, TH
Quantum Cosmology and Holography!
Euclidean de SiYer Euclidean anS-‐de SiYer
Lorentzian de SiYer
Apply ADS/CFT !
Hartle, TH, 12
A = exp(IRegAdS)
Quantum Cosmology and Holography!
Euclidean de SiYer
Lorentzian de SiYer
Boundary QFT
Horowitz, Maldacena, 04
exp(�IRegAdS [h,
˜�]/~) = ZQFT [h, ˜�]Eucl AdS/CFT:
Conclusion • The wave func-on of the universe implies a prior over
models, backgrounds and observables in infla-on
• The no-‐boundary prior favors plateau-‐like poten-als • Anthropic selec-on is part of the general framework for
predic-on in quantum cosmology • The no-‐boundary prior restores Weinberg’s successful
anthropic predic-on of Λ even when Q varies
• The structure of the landscape and a precise formula-on of Ψ remain important challenges