Cosmology of String
Theory:
Inflation and Beyond
F. Quevedo, Cambridge. UNIVERSENET 2007. Mytilene
OUTLINE
• String Theory and 4D Inflation
FQ hepth/0210292
• Moduli Stabilization and the String Landscape
(KKLT and LARGE volume scenarios)
• Inflation and Moduli Stabilization (open string vs
closed string inflaton). C. P. Burgess
0708.2865 [hep-th
[hep-th]]
• After Inflation
MOTIVATION
• Inflation: very successful but is only ad-
hoc scenario 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,
Binetruy-Gaillard, Banks et al
• Or V too steep:
Brustein-Steinhardt
Brustein-Steinhardt
New Problems:
• Overshooting
(natural to end up in runaway)
Brustein-Steinhardt
Brustein-Steinhardt
• Cosmological Moduli Problem
Coughlan et al. 82
(moduli overclose the universe or ruin Banks et al. 94
nucleosynthesis) De Carlos et al. 93
(t>1995) More moduli!
Open string moduli:
Brane separation
Also Wilson Lines
See Avgoustidis talk
• t=199 : 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.
tachyon
Y
Tachyon complex topological defects Sen,
Sen, Burgess
et al.
D (p-2) branes cosmic strings !
Tye et al.
Copeland et al.
Intersecting Brane Inflation
Garcia-Bellido
Garcia-Bellido et al.
Gomez-Reino
Gomez-Reino,, Zavala
Y: Inflaton
End of inflation: tachyon!!
Also: D3-D7 inflation Kallosh et al.
Wilson Line Inflation
Avgoustidis-Cremades-FQ
T-Duality:
Dp-Branes D(p+1)-Branes
Brane Separation Wilson Lines
Angles Magnetic Fluxes
Brane inflation Wilson Line Inflation
Moduli Stabilisation and
Supersymmetry Breaking
The Problem
• String/M-Theory unique but has many solutions
or vacua.
• 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
CHSW Complex structure U
Wilson Lines W
• 1986<t<1991 Gaugino condensation and T-
duality
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, …
KKLT Scenario
…GKP, KKLT, …
Type IIB String on Calabi-Yau orientifold
Turn on Fluxes
∫ a F3 = n a ∫ b H3 = m b Size of cycle a = Ua
Superpotential W = ∫ G3 Λ Ω, G3 = F3 –iS H3
Scalar Potential: V= eK |DaW|2
Minimum DaW = 0 Fixes Ua and S
T moduli unfixed: No-Scale models GKP
4D Compactifications
• To fix Kähler moduli: Non-perturbative D7 effects
Fluxes Non-perturbative
Volume
SUSY AdS minimum
(W0 << 1)
• Lifting to de Sitter (add anti D3 branes, D-terms, etc.)
KKLT, BKQ, SS
SUSY breaking term
axion volume
ALL MODULI STABILISED !
Universe
D3 Brane
or
D7 Brane
Exponentially Large
Volumes
Argument:
• In general:
• Then:
• Usually V0 dominates but V0=0
(no-scale )
• Dominant term is VJ unless
W0<<1 (KKLT)
Exponentially Large Volumes
BBCQ, CQS
• Perturbative corrections to K
• At least two Kähler moduli (h21>h11>1) Example :
Non SUSY AdS
W0~1-10
String scale: Ms2=Mp2/V
Non SUSY AdS
W0~1-10
String scale: Ms2=Mp2/V
KKLT AdS
Non SUSY AdS
Both minima
close
W0~10-10
W0<10-11
The Landscape
The Landscape
• Huge number of
discrete vacua >10500
• Statistics AD, DD, DDF, GKTT,CQ,BGHLW
• Randall-Sundrum GKP
warping from strings!
• 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
Interesting But…
• This is NOT the slow-roll inflation that we
are after.
• Where are we in the landscape?
Modular Model Building
(Bottom up approach)
The Standard Model in the CY
Realistic Models
AIQU, CG-MQU,
H. Verlinde et al.
Bottom-up Approach
Aldazabal,Ibanez,
Aldazabal,Ibanez, FQ, Uranga 2000
Verlinde,Wijnholt 2006
Local (brane) Properties Global (bulk) Properties
• Gauge group • Moduli Stabilisation
• Chiral spectrum • SUSY Breaking
• Yukawa couplings • Soft terms
• Gauge unification • Cosmological constant
• Proton stability • Inflation
• Baryogenesis
• Reheating
PHENOMENOLOGY
(From Strings to LHC)
(LARGE Volume models)
Standard Model on D7 Branes
• Solve hierarchy problem Mstring = 1011 GeV!
• W0~1 (no fine tuning)
• Kahler potential for chiral matter computed
Conlon,
Conlon, Cremades,
Cremades, FQ (2006)
Chiral Matter on D7 Branes
Soft SUSY Breaking terms
Conlon et al.
• Universality!
Simplest case • No extra CP violation!
λ=1/3 • Mi = m3/2 / log (Mp/m3/2)
• String scale 1011 GeV
• Solves hierarchy problem!
Stringy source of universality
(approximate)
CP Violation
Physical phases vanish !
Also: Anomaly mediation suppressed !!!
From Strings to LHC data
CKSAQ 0705.3460[hep-ph],
• Stabilise Moduli
• SUSY broken with hierarchy
• “Realistic” Observable sector
• Soft SUSY Breaking terms@Ms
• RG-Running of Soft terms to TeV (softsusy)
• Event Generators (PYTHIA-Herwig)
• Detector Simulators (PGS, GEANT) 10-1 fb
• Data Analysis and reconstruction (Root) 100-1 fb
• Estimate overall uncertainty
Low energy spectrum
COSMOLOGY
(Inflation, Cosmological moduli
problem, etc.)
Brane-Antibrane Inflation
BMNRQZ, DSS
KKLMMT, HKP, KTW,
FT, BCSQ
φ inflaton field D3 Brane
φ
BRANE - ANTIBRANE INFLATION
All branes inflate while two approach
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 Burgess, Cline,
Stoica,
Stoica, FQ
Ms~ 1015 GeV
ns~1.05
ns<1 (Cline-Stoica
(Cline-Stoica))
Needs at least two throats !
Also: D3-D7 on K3xT2 Kallosh et al.
DBI in the sky Silverstein-Tong, Chen, Tye et al.
Tachyonic Inflation
Sen,
Sen, Raeymakers,
Raeymakers, Cremades-Sinha-FQ
A,B depend on warping (fluxes) and E&M fields on non-
BPS brane. If A,B~1 no slow-roll
AB large slow-roll
No fine-tuning! But need large fluxes
Racetrack Inflation
Blanco-Pillado
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,
Lalak, Ross, Sarkar
Better Racetrack Inflation
Blanco-Pillado
Blanco-Pillado et al.
Douglas et al.
Explicitly derived model
Similar physics
Kähler Moduli Inflation
Conlon-FQ
Bond-Kofman-Prokushkin
Bond-Kofman-Prokushkin
Calabi-Yau:
h21>h11>2
Small field inflation
No fine-tuning!!
0.960<n<0.967
V
GUT scale Ms?, Loops?
volume τn
MODULI INFLATION
Candidate Inflatons: Closed
string modes
Kahler Moduli (size/axion)
Complex structure
moduli?
Open Questions
• Inflation possible but not generic (fine
tuning)
• Initial conditions/Singularity,…
• Non tensor perturbations (r=s/t<<<1)?
Baumann, McCalister
• Tension phenomenology vs cosmology
Gravitino mass 1 TeV/Gravitino mass >> 1 TeV ??
Ross, Sarkar
Kallosh-Linde
(string scale 10 11 GeV/ string scale ~ GUT scale)
Possible ways out
• Low scale inflation? German, Ross, Sarkar, …
• Runaway before reheating?
Conlon et al.
After Inflation
Physics of Moduli Fields
• Dilaton and Complex
Structure
Moduli masses:
• Small (heavy) Kahler moduli
• Large (light) Kahler modulus
Physical Fields
Decay Rates
Other Cosmological Implications
J.Conlon, FQ
• Cosmological moduli problem
DCQR,
DCQR, BKN
U,S: trapped at their minimum
T: except for volume, heavy ad decay fast ! (No
CMP nor gravitino overproduction)
Volume: (mass MeV) CMP
• Observational implications of light volume
modulus?
Gamma rays, e+-e-
Solution of CMP?
Thermal Inflation
Lyth+Stewart (1995)
Number of e-folds
N~10 dilutes moduli
Late time implications:
Diffuse Gamma Ray Background
The 511 keV Line
INTEGRAL/ SPI 511 keV line
Light Modulus χ: Dark matter?
Mass 1MeV, coupling to electrons dominant
511 keV from volume modulus decay? (prediction!)
Intensity
INTEGRAL
CONCLUSIONS
• Exciting times for string cosmology/phenomenology!
• Soft terms calculable rich phenomenology
• Distinctive moduli cosmology
• Concrete models of inflation (closed vs open string inflaton)
• Model independent signatures: cosmic strings, no
tensor modes, light modulus (CMP, 511 keV? Prediction!)
• Many open questions
MGUT vs 1011 GeV scales?
Fully realistic model?...
• Alternatives to inflation?
