Inflationary Scenarios from String Theory

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Inflationary Scenarios from String Theory
F. Quevedo Cambridge COSMO 2005
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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?

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HISTORY

• tlt1986 Calabi-Yau String Compactifications Many
  free moduli (size and shape of extra dimensions)
  from gmn, Bmn, f, AmI
• 1986lttlt1991 Geometric moduli candidate for
  inflaton fields. But no potentials (V0).
• Or V too steep

Candelas et al.
Dilaton S, Kähler T Complex structure U Wilson
lines W
Binetruy-Gaillard, Banks et al
Brustein-Steinhardt
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• t1998 More moduli! D-brane inflation. But
  V0 or non-calculable.
• t2001 Brane/Antibrane inflation

Dvali-Tye
Burgess et al., Dvali et al
Generically no slow roll, but
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End of inflation Open string tachyon
Burgess et al.
V
tachyon
Y
Tachyon complex topological defects D
(p-2) branes cosmic strings !
Sen, Burgess et al.
Tye et al. Copeland et al.
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Intersecting Brane Inflation
Garcia-Bellido et al.
Y Inflaton End of inflation tachyon
Also D3-D7 inflation
Kallosh et al.
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Outstanding Problem

• Moduli Stabilization

A Solution turn-on fluxes
tgt 2003 KKLT Scenario
GKP, KKLT,
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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 ? O, G3 F3 iS
  H3
• Scalar Potential V eK DaW2
• Minimum DaW 0 Fixes Ua
  and S
• T moduli unfixed No-Scale
  models

Size of cycle a Ua
GKP
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• To fix Kähler moduli Non-perturbative D7 effects

Non-perturbative
Fluxes
Volume
SUSY AdS minimum
(W0 ltlt 1)
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• Lifting to de Sitter (add anti D3 branes,
  D-terms, etc.)

KKLT, BKQ, SS
SUSY breaking term
V
axion
volume
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The Landscape

• Huge number of discrete vacua gt10500
• Statistics
• Randall-Sundrum warping from strings!
• Non SUSY de Sitter
• Dark energy?
• SM on D3/D7branes
• Soft SUSY breaking?
• Inflation?

AD, DD, DDF, GKTT,CQ,BGHLW
GKP
BP
CG-MQU
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Realistic Models
CG-MQU, CSU
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Exponentially Large Volumes
BBCQ, CQS

• At least two Kähler moduli (h21gth11gt1)
• Perturbative corrections to K

Example
Exponentially large !
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Non SUSY AdS
W01-10 String scale Ms2Mp2/V
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KKLT AdS
Non SUSY AdS
Both minima merge
W010-10
W0lt10-11
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Inflation and Moduli Stabilization
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Brane-Antibrane Inflation
KKLMMT, HKP, KTW, FT, BCSQ,
f inflaton field
D3 Brane
f
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Slow-roll (large field) inflation possible. Need
1/1000 fine tuning of parameters to get
60-efoldings (?-problem)
N60, dH10-5 for Ms 1015 GeV ns1.05
Burgess, Cline, Stoica, FQ
Needs at least two throats !
Kallosh et al.
Also D3-D7 on K3xT2 DBI in the sky
Silverstein-Tong, Chen
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Warped Tachyonic Inflation
Sen, Raeymakers, Cremades-Sinha-FQ
A,B depend on warping (fluxes) and EM fields on
non-BPS brane. If A,B1 no slow-roll
AB large slow-roll
No fine-tuning! But need large fluxes
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INITIAL CONDITIONS
Sens open string completeness conjecture t
-t
Pre big-bang ! ?
Inflation and compactification or
big-crunch/bang and decompactification ! ?
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Racetrack Inflation
Blanco-Pillado et al.
Topological eternal inflation !
Slow roll if 1/1000 fine tuning, N60, dH10-5
for Ms1015 GeV ns 0.95
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Improved Racetrack
Blanco-Pillado et al.
Douglas et al.
Explicitly derived model Similar physics
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Kähler Moduli Inflation
Conlon-FQ
Any Calabi-Yau h21gth11gt2
V
Large field inflation No fine-tuning!! 0.960ltnlt0.9
67
tn
volume
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CONCLUSIONS

• Exciting times
• Type IIB Several inflationary scenarios,
• Inflaton Kahler modulus, brane sparation,
  tachyon, Wilson lines , Complex structure moduli
  (?).
• Reheating
• Extensions to other string theories (Becker et
  al)
• Initial conditions
• Overshooting problem,.

Open questions