Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!!...

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Quantum Cosmology: Prediction vs Observation Thomas Hertog Institute for Theoretical Physics University of Leuven, Belgium COSMO2013, Cambridge

Transcript of Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!!...

Page 1: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

Quantum Cosmology: Prediction vs Observation

Thomas Hertog!  

Institute for Theoretical Physics University of Leuven, Belgium!

COSMO2013,  Cambridge  

Page 2: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*
Page 3: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*
Page 4: Quantum Cosmology · 2013. 9. 17. · 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!!

Page 5: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

f

VHfLPREDICTING a PRIOR for Inflation!

Page 6: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

f

VHfLPREDICTING a PRIOR for Inflation!

?  ?  

Page 7: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

f

VHfLPREDICTING a PRIOR for Inflation!

Ψ è relative weighting è robust predictions

Page 8: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

Outline

� Quantum Cosmology: Framework! �  " è A prior for inflation!

�  " è Anthropic selection !

�  Holography: towards a precise form of " !

!

Page 9: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

(g,φ)  TIME  

Classical   Quantum  

RADIUS  

singular  regular  

No-Boundary Wave Function!Hartle,  Hawking,  1983  

Page 10: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

No-Boundary Wave Function!

[

3g,�] ⇡ exp

��IE [

3g,�]/~�

(3g,�)

Page 11: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

No-Boundary Wave Function!

REAL  

COMPLEX  

(3g,�)

[

3g,�] ⇡ exp

��IE [

3g,�]/~�= A exp(iS)

Page 12: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

Emergent classical cosmology!

[

3g,�] ⇡ A exp(iS)

|rA| ⌧ |rS| Classical evolution!

MULTIVERSE  pq = rqS

Phist / A2= exp(�2IR/~)

Page 13: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

Inflation!

Inflation emerges as a prediction!

Hartle,  Hawking,  TH,  2008  

h=mφ  V (�) =

1

2m2�2

è  Ψ  implies  vacuum  selec-on  

Page 14: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

Probability distribution!

Slava’s talk

è  Predictions for observations

| |2 / exp

✓⇡

4V (�0)

◆exp

⇣� ✏

H2n3⇣2n

Page 15: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

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

Page 16: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

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 )

Page 17: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

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

Page 18: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

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  

Page 19: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

8  HH  

Planck  2013,  XXII  

Different  regions  in    a  single  theory  !  

Page 20: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

8  HH  

tunneling  

Assuming an unbiased landscape potential

Planck  2013,  XXII  

Page 21: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

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  

Page 22: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

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  

Page 23: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

Open Questions

�  Structure landscape potential � Formulation " beyond WKB limit!!�  Unique " ?!

McAllister  et  al.  Agarwal  et  al.  Pedro,  Westphal  

Page 24: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

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  

Page 25: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

Quantum Cosmology and Holography!

Euclidean  de  SiYer   Euclidean  anS-­‐de  SiYer  

Lorentzian  de  SiYer  

Apply  ADS/CFT  !  

Hartle,  TH,  12  

A = exp(IRegAdS)

Page 26: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

Quantum Cosmology and Holography!

Euclidean  de  SiYer  

Lorentzian  de  SiYer  

Boundary  QFT  

Horowitz,  Maldacena,  04  

exp(�IRegAdS [h,

˜�]/~) = ZQFT [h, ˜�]Eucl  AdS/CFT:  

Page 27: Quantum Cosmology · 2013. 9. 17. · Quantum Cosmology: Prediction vs Observation Thomas Hertog!! Institute for Theoretical Physics University of Leuven, Belgium! COSMO2013,*Cambridge*

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