Transcript Ciencia en el Tercer Mundo/El Paisaje de Cuerdas

Cosmology and String
Theory
F. Quevedo
Cambridge
CORFU 2005
OUTLINE
String Cosmology before 2003
FQ hepth/0210292
The KKLT Scenario and the String
Landscape
Inflation and Moduli Stabilization
STRING COSMOLOGY
String theory is fundamental then it should
have important implications in early
universe
Quantum gravity
Big bang or before
Experimental tests of the theory?
OBSERVATIONAL
CHALLENGES
CMB Anisotropies
EXPERIMENTAL
EVIDENCE FOR Λ>0
Ω = ΩΛ + ΩM + ΩK =
Ω = ρ/ρc relative energy density
K = -1,0,1 open, flat, closed universe
ΩΛ ~ 0.7, ΩM~ 0.3, Ωk~ 0
1
PROBLEM
Do not understand the theory in
time dependent backgrounds !!!
Effective Field Theories
General Aspects
Branderberger-Vafa Scenario ((S1)9 x time)
T-duality
Minimal distance !
Winding modes
D=4 (since 2+2=4)!
Pre Big-Bang Cosmology
t=0 singularity + strong coupling
Gasperini, Veneziano,…
String Theory and 4D
Inflation
MOTIVATION
Inflation: very successful but only
scenarios in search of a theory
String theory: fundamental theory but
lacks experimental tests.
Is it possible to `derive’ inflation from string
theory?
Need to compute scalar potential from String
theory satisfying slow-roll conditions:
Number of e-folds N>60
Density perturbations
HISTORY
t<1986 Calabi-Yau String Compactifications: Many free moduli (size
and shape of extra dimensions) from gmn, Bmn, φ, AmI
Candelas et al.
Dilaton S,
Kähler T
Complex structure U
Wilson lines W
1986<t<1991 Geometric moduli: candidate for inflaton fields. But no
potentials (V=0).
Binetruy-Gaillard, Banks et al
Or V too steep:
Brustein-Steinhardt
New Problems:
Overshooting
(natural to end up in runaway)
Brustein-Steinhardt
Coughlan et al.
Cosmological Moduli Problem
Banks et al.
De Carlos et al.
(moduli overclose the universe or ruin
nucleosynthesis)
t=1995-1998
The Brane World
ADD, Horava-Witten,…
t=1998 More moduli! : D-brane inflation. But V=0 or non-calculable.
Dvali-Tye
t=2001 Brane/Antibrane inflation:
Burgess et al., Dvali et al
Generically no slow roll,
but…
End of inflation: Open string tachyon
Burgess
et al.
V
tachyon
Y
Tachyon complex
D (p-2) branes
topological defects
cosmic strings !
Tye et al.
Copeland et al.
Sen, Burgess
et al.
Intersecting Brane Inflation
Garcia-Bellido et al.
Y: Inflaton
End of inflation: tachyon
Also: D3-D7 inflation
Kallosh et al.
Ekpyrotic/Cyclic Scenario
Horava Witten 11D
a(0)=0 weak coupling (bounce?)
But: singularity? Potential by hand,…
Outstanding Problem
Moduli Stabilization
A Solution: turn-on fluxes
t> 2003
KKLT Scenario
…GKP, KKLT, …
Moduli Stabilization
The Problem
String/M-Theory unique but has many solutions
or vacua.
Some solutions resemble the Standard Model
and MSSM.
Degeneracy : Discrete + Continuous (SUSY) .
Outstanding Problems:
SUSY breaking + Vacuum degeneracy.
History
t<1986 Calabi-Yau String Compactifications: Many free
moduli (size and shape of extra dimensions)
Dilaton S, Kähler T
Complex structure U
CHSW
1986<t<1991 Gaugino condensation and Tduality
DIN, DRSW, K, FILQ, FMTV
Fix S and one T
1991<t<2002 More moduli! (D-brane positions)
t>2002 GKP/ KKLT : Fluxes fix moduli
…GKP, KKLT, …
4D Compactifications + Fluxes
KKLT Scenario
…GKP, KKLT, …
Type IIB String on Calabi-Yau orientifold
Turn on Fluxes
∫a F3 = n a
∫b H3 = m b
Superpotential W = ∫ G3 Λ Ω,
Scalar Potential:
Size of cycle a = Ua
G3 = F3 –iS H3
V= eK |DaW|2
Minimum DaW = 0 Fixes Ua and S
T moduli unfixed: No-Scale models
GKP
To fix Kähler moduli: Non-perturbative D7 effects
Fluxes
Volume
SUSY AdS minimum
(W0 << 1)
Non-perturbative
Multi-throat
compactification
Lifting to de Sitter (add anti D3 branes, D-terms, etc.)
KKLT, BKQ, SS, VZ
SUSY breaking term
V
axion
volume
The Landscape
Huge number of discrete
vacua >10500
Statistics AD, DD, DDF, GKTT,CQ,BGHLW
Randall-Sundrum
warping from strings! GKP
Non SUSY de Sitter
Dark energy? BP
`SM’ on D3/D7branes CG-MQU
Soft SUSY breaking?
Inflation?
Populating the Landscape
Classical Solutions
Quantum decay
(tunnel efect)
Multiverse and Eternal Inflation
Realistic Models
CG-MQU, CSU
Exponentially Large Volumes
BBCQ, CQS
At least two Kähler moduli (h21>h11>1)
Perturbative corrections to K
Example :
Exponentially large !
Non SUSY AdS
W0~1-10
String scale: Ms2=Mp2/V
KKLT AdS
Non SUSY AdS
Both minima
merge
W0~10-10
W0<10-11
Soft SUSY Breaking
From KKLT not explicit model but interesting general
behaviour (D/F term breaking, AMSB, …) CFNOP,CJO
From lifting of large volume models
CQS
Matter on D3
Ms~1013 GeV
Gaugino masses ~ 102 GeV, scalars m ~ 107 GeV
Ms=MGUT viable if warping,
Ms=Tev `viable’ if SM anti D-brane (but 5th force and cmp?)
Inflation and Moduli
Stabilization
Brane-Antibrane Inflation
KKLMMT, HKP, KTW,
FT, BCSQ, …
φ inflaton field
D3 Brane
φ
Slow-roll (large field) inflation possible.
Need 1/1000 fine tuning of parameters to
get 60-efoldings (η-problem)
N~60, δH~10-5 for
Ms~ 1015 GeV
ns~1.05
Needs at least two throats !
Also: D3-D7 on K3xT2 Kallosh et al.
DBI in the sky
Silverstein-Tong, Chen
Burgess, Cline,
Stoica, FQ
Warped Tachyonic Inflation
Sen, Raeymakers, Cremades-Sinha-FQ
A,B depend on warping (fluxes) and E&M fields on nonBPS brane. If A,B~1 no slow-roll
AB large
slow-roll
No fine-tuning! But need large fluxes
INITIAL CONDITIONS
Sen’s open string
completeness
conjecture
t
-t
Pre big-bang ! ?
Inflation and compactification or big-crunch/bang
and decompactification ! ?
Racetrack Inflation
Blanco-Pillado et al.
Topological eternal inflation !
Slow roll if 1/1000 fine tuning,
N~60, δH~10-5 for Ms~1015 GeV
ns ~ 0.95
Also for W0=0 if add matter
Lalak, Ross, Sarkar
Improved Racetrack
Blanco-Pillado et al.
Douglas et al.
Explicitly derived model
Similar physics
Kähler Moduli Inflation
Conlon-FQ
Any Calabi-Yau:
h21>h11>2
V
Large field inflation
No fine-tuning!!
0.960<n<0.967
volume
τn
CONCLUSIONS
Exciting times
Type IIB: Several inflationary scenarios,
Inflaton: Kahler modulus, brane sparation, tachyon, Wilson lines ,
Complex structure moduli (?).
OPEN QUESTIONS
Reheating
Extensions to other string theories (Becker et al)
Initial conditions
Overshooting problem,….