The%20LARGE%20Volume%20Scenario:%20Realisation%20and%20Cosmological%20Implications

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The LARGE Volume Scenario Realisation and
Cosmological Implications
F. Quevedo, Cambridge. Liverpool, March 2008.

• M. Cicoli, J. Conlon, FQ, 0708.1873 hep-th
  to appear
• J. Conlon, R. Kallosh, A. Linde, FQ, to appear

Related talks E. Plauschinn and E. Palti
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String Phenomenology

• Explicit Realistic Models
• (SU(3)xSU(2)xU(1), 3 families, etc.)
• Model Independent Issues
• (axions, no-global symmetries,.,SUSY breaking,
  moduli stabilisation,)
• 4D Effective Actions
• (Explicit form of K, W, f. For N1
  compactifications)

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Why LARGE volume?

• Effective field theory robust
• Phenomenology M2PlanckM2string V

V104 MstringMGUT1017GeV V1030
Mstring1 TeV V1015 Mstring1011 GeV (Also
RS warping !)
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MODULI STABILISATION?
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Exponentially Large Volumes in IIB
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Perturbative vs Non perturbative

• In general
• Then
• Usually V0 dominates but V00 (no-scale
  )
• Dominant term is VJ unless W0ltlt1 (KKLT)

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Exponentially Large Volumes
BBCQ, CQS (2005)

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

Example
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as2p/gs N
Exponentially large volumen !!!
String scale Ms2M2Planck/V W01-10 Ms1 TeV
problematic from 5th force
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Universe D3 Brane or D7 Brane
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Standard Model on D7 Branes

• Solve hierarchy problem Mstring 1011 GeV!
• W01 (no fine tuning)
• Kahler potential for chiral matter computed

Conlon, Cremades, FQ (2006)
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The Standard Model in the CY
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Chiral Matter on D7 Branes Soft SUSY Breaking
terms
Conlon et al.

• Universality!
• No extra CP violation!
• Mi m3/2 / log (Mp/m3/2)
• String scale 1011 GeV
• Solves hierarchy problem!

Simplest case ?1/3
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General Conditions for LARGE Volume

• h12 gt h11 gt 1
• At least one blow-up mode (point-like
  singularity)
• Blow-up mode fixed by non-perturbative effects,
  volume by alpha corrections
• For Nsmall blow-up modes, there are
  Lh11-Nsmall-1 flat directions at tree-level
• These directions are usually lifted by
  perturbative effects
• L moduli lighter than
  volume!

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String Loop Corrections
Berg-Haack-Kors Berg-Haack-Pajer
Leading order correction for V is alpha but
string loops relevant to fix other moduli
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Example 1
Blumenhagen et al
TauSM
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Example 2 K3 Fibrations

• K3 Fibration with 2 Kahler moduli 1,1,2,2,6
  model
• No LARGE volume

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• K3 Fibration with 3 Kahler moduli (one blow- up)
• tau3 small, tau 1 and tau 2 LARGE

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V
W
W
Volume, W
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COSMOLOGY

• (Inflation, Cosmological moduli problem, etc.)

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BRANE - ANTIBRANE INFLATION
All branes inflate while two approach Inflaton
Open string mode (talks by R. Gregory, M. Haack
and H. Stoica)
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KAHLER MODULI INFLATION

• Candidate Inflatons Closed string modes
• Kahler Moduli (size/axion)
• Small modulus inflaton

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Kähler Moduli Inflation
Conlon-FQ Bond-Kofman-Prokushkin
Calabi-Yau h21gth11gt2
Small field inflation No fine-tuning!! 0.960ltnlt0.9
67
V
tn
volume
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Open Questions

• Loop effects tend to spoil flatness
• Non tensor perturbations (rT/Sltltlt1)?
• Tension phenomenology vs cosmology

Gravitino mass 1 TeV/Gravitino mass gtgt 1 TeV
?? (string scale 10 11 GeV/ string scale GUT
scale)
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Low Energy SUSY vs Inflation

• Low scale inflation?
• Runaway before reheating?

Ross et al,
Conlon, Kallosh, Linde, FQ
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No Overshooting problem!!!
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New Candidate Inflatons

• Lh11-Nsmall-1 almost flat directions are light
• MassV-5/3lt Volume modulus mass
• mV-3/2H
• Recall ? mass2/H

Cicoli et al.
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After Inflation
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Physics of Moduli Fields

• Dilaton and Complex Structure
• Small (heavy) Kahler moduli
• Large (light) Kahler modulus

Moduli masses
Volume axion mexp(-V)ltlt10-33 eV (equality if
MstringMGUT)!
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Summary of couplings
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Other Cosmological Implications
J.Conlon, FQ

• Cosmological moduli problem
• Observational implications of light volume
  modulus?

DCQR, BKN
U,S trapped at their minimum T except for
volume, heavy and decay fast ! (No CMP nor
gravitino overproduction) Volume (mass MeV) CMP
Gamma rays, e-e-
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The 511 keV Line
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INTEGRAL/ SPI 511 keV line
Light Modulus ? Dark matter? Mass 1MeV,
coupling to electrons dominant 511 keV from
volume modulus decay? (prediction!) BUT almost
ruled out 2 months ago!!!
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Intensity
INTEGRAL
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General Picture

• Nsmall heavy Kahler moduli (cosmological
  harmless)
• Volume modulus (CMP 511 keV line predicted
  monochromatic line!) (see Boyarski et al)
• Lh11-Nsmall-1 lighter moduli (candidate
  inflatons, CMP, new monochromatic lines!!
  (observable?))
• CMP (late low energy inflation?)

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Conclusions

• Non-perturbative effects fix only a fraction of
  Kahler moduli (Nsmall)
• Alpha effects fix volume to exponentially large
  values (Both LARGE volume and large warping in
  the same class of models!?)
• Loop corrections needed to fix the rest of Kahler
  moduli
• Interesting phenomenology/cosmology
• Astrophysics (forest of monochromatic lines?)
• Fully realistic model?

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Solution of CMP?Thermal Inflation
LythStewart (1995)
Number of e-folds
N10 dilutes moduli