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The LARGE Volume Scenario: Realisation and Cosmological
Implications
M. Cicoli, J. Conlon, FQ, 0708.1873 [hep-th] + to appearJ. Conlon, R. Kallosh, A. Linde, FQ, to appear
F. Quevedo, Cambridge. Liverpool, March 2008.
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 N=1 compactifications)
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Why LARGE volume?
• Effective field theory robust
• Phenomenology M2
Planck=M2
string V
V=104 Mstring=MGUT=1017
GeV
V=1030 Mstring=1 TeV
V=1015 Mstring=1011
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 V0=0 (no-scale )
• Dominant term is VJ unless W0<<1 (KKLT)
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Exponentially Large Volumes
• Perturbative (alpha’) corrections to K
• At least two Kähler moduli (h21>h11>1)Example :
BBCQ, CQS (2005)BBCQ, CQS (2005)
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String scale: Ms2=M2
Planck/V
W0~1-10
Ms=1 TeV problematic from 5th force
Exponentially large volumen !!!
as~2π/gs N
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UniverseUniverse
D3 BraneD3 Brane
oror
D7 BraneD7 Brane
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Standard Model on D7 Branes
• Solve hierarchy problem Mstring = 1011 GeV!
• W0~1 (no fine tuning)
• Kahler potential for chiral matter computedConlon, Cremades, FQ (2006) Conlon, Cremades, FQ (2006)
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The Standard Model in the CYThe Standard Model in the CY
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Chiral Matter on D7 Branes
Soft SUSY Breaking terms
• Universality!Universality!• No extra CP violation!No extra CP violation!
• MMii = m = m3/23/2 / log (Mp/m / log (Mp/m3/23/2))
• String scale 10String scale 101111 GeV GeV • Solves hierarchy problem!Solves hierarchy problem!
Conlon et al.Conlon et al.
Simplest case λ=1/3
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General Conditions for LARGE Volume
• h12 > h11 > 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 L=h11-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-KorsBerg-Haack-Kors
Berg-Haack-Pajer Berg-Haack-Pajer
Leading order correction for V is alpha’ but string loops relevant to fix other moduli
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TauSM
Example 1Example 1Blumenhagen et alBlumenhagen et al
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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
Volume,
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COSMOLOGY
(Inflation, Cosmological moduli problem, etc.)
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BRANE - ANTIBRANE INFLATIONBRANE - ANTIBRANE INFLATION
All branes inflate while two approachAll branes inflate while two approach
Inflaton: Open string mode Inflaton: Open string mode (talks by R. Gregory, M. Haack and H. Stoica)(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
Calabi-Yau:
h2121>>h1111>2
volume τn
V
Conlon-FQ Conlon-FQ
Bond-Kofman-ProkushkinBond-Kofman-Prokushkin
Small field inflation
No fine-tuning!!
0.960<n<0.967
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Open Questions
• Loop effects tend to spoil flatness
• Non tensor perturbations (r=T/S<<<1)?
• Tension phenomenology vs cosmology
Gravitino mass 1 TeV/Gravitino mass >> 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? Conlon, Kallosh, Linde, FQ
Ross et al, …
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No Overshooting problem!!!
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New Candidate Inflatons
• L=h11-Nsmall-1 `almost’ flat directions are light
• Mass=V-5/3< Volume modulus mass
m=V-3/2~H
• Recall η ~ 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 m~exp(-V)<<10-33 eV (equality if Mstring=MGUT)!
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Summary of couplings
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Other Cosmological Implications
• Cosmological moduli problem
• Observational implications of light volume modulus?
U,S: trapped at their minimumU,S: trapped at their minimum
T: except for volume, heavy and decay fast ! (No T: except for volume, heavy and decay fast ! (No CMP nor gravitino overproduction)CMP nor gravitino overproduction)
Volume: (mass MeV) CMP Volume: (mass MeV) CMP
Gamma rays, e+-e-
J.Conlon, FQJ.Conlon, FQ
DCQR, BKNDCQR, BKN
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The 511 keV LineThe 511 keV Line
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INTEGRAL/ SPI 511 keV lineINTEGRAL/ SPI 511 keV line
Light Modulus χ: Dark matter?
Mass 1MeV, coupling to electrons dominant
511 keV from volume modulus decay? (prediction!)511 keV from volume modulus decay? (prediction!)
BUT `almost’ ruled out 2 months ago!!!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)
• L=h11-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
Lyth+Stewart (1995)Lyth+Stewart (1995)
Number of e-folds
N~10 dilutes moduli