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

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)

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 !)

MODULI STABILISATION?

Exponentially Large Volumes in IIB

Perturbative vs Non perturbative :

• In general:

• Then:

• Usually V0 dominates but V0=0 (no-scale )

• Dominant term is VJ unless W0<<1 (KKLT)

Exponentially Large Volumes

• Perturbative (alpha’) corrections to K

• At least two Kähler moduli (h21>h11>1)Example :

BBCQ, CQS (2005)BBCQ, CQS (2005)

String scale: Ms2=M2

Planck/V

W0~1-10

Ms=1 TeV problematic from 5th force

Exponentially large volumen !!!

as~2π/gs N

UniverseUniverse

D3 BraneD3 Brane

oror

D7 BraneD7 Brane

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)

The Standard Model in the CYThe Standard Model in the CY

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

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!

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

TauSM

Example 1Example 1Blumenhagen et alBlumenhagen et al

Example 2: K3 Fibrations

• K3 Fibration with 2 Kahler moduli [1,1,2,2,6] model

• No LARGE volume

• K3 Fibration with 3 Kahler moduli (one blow- up)

• tau3 small, tau 1 and tau 2 LARGE

V

Volume,

COSMOLOGY

(Inflation, Cosmological moduli problem, etc.)

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)

KAHLER MODULI INFLATION

Candidate Inflatons: Closed string modes

Kahler Moduli (size/axion)

Small modulus inflaton

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

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)

Low Energy SUSY vs Inflation

• Low scale inflation?

• Runaway before reheating? Conlon, Kallosh, Linde, FQ

Ross et al, …

No Overshooting problem!!!

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.

After Inflation

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)!

Summary of couplings

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

The 511 keV LineThe 511 keV Line

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!!!

Intensity

INTEGRAL

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?)

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?

Solution of CMP?Thermal Inflation

Lyth+Stewart (1995)Lyth+Stewart (1995)

Number of e-folds

N~10 dilutes moduli