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Cosmological Moduli Problem and Double Thermal Inflation in Large Volume Scenario KC, W.I. Park & C.S. Shin, arXiv:1207.xxxx. Kiwoon Choi (KAIST) String Pheno 2012 (June 25, Cambridge). Outline 1) Introduction

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Cosmological Moduli Problem and DoubleThermal Inflation

in Large Volume Scenario

KC, W.I. Park & C.S. Shin, arXiv:1207.xxxx

Kiwoon Choi


String Pheno 2012

(June 25, Cambridge)


1) Introduction

* Local GUT in large bulk volume whichis responsible for MGUT/MPlanck ~ 10-2

* Cosmological moduli problem associated with the large volume modulus &

double thermal inflation as a solution

2) Large volume scenario (LVS) with double thermal inflation

3) Conclusion


One of the most attractive features of TeV scale SUSY is the successful unification

of gauge couplings at MGUT ~ 1016 GeV.

On the other hand, this value of MGUT is meaningfully lower than MPlanck ~ 1018 GeV,

which might require an explanation.

One possible explanation :

Gravity in large bulk spaceand local GUT on branes (at boundary or small cycle)

Horava & Witten, …

In 4D effective theory, the scale hierarchy MGUT/MPlanck ~ 10-2 is realized through

a large VEV of the bulk volume modulus :

Kaplunovsky & Louis

( )

Such large VEV of the volume modulus implies that its scalar potential is relatively

flat (at least near the minimum), so the volume modulus is relatively light.


Cosmological moduli problem

Coughlan, Fischler, Kolb, Raby, Ross (1983); de Carlos et al (1993); Banks et al (1994)

Hubble-induced moduli potential in the early Universe:

 Coherent moduli oscillation of with an initial amplitude

Huge amount of moduli production:

On the other hand, depending upon the moduli lifetime, moduli density is severely

constrained by

* Relic mass density (nearly stable moduli)

* Diffuse X rays and gamma rays from moduli decay

* Spectral distortion of CMBR by moduli decay

* Destruction of light elements after the BBN

Constraints from BBN, CMBR, X & gamma rays, relic mass density:

Compare with

KC, Chun & Kim (1998)

Solutions: density:

* Moduli decay before the BBN :

* Moduli are diluted enough by a late entropy production before the BBN:

Thermal Inflation Lyth & Stewart (1995)

* Short-lived moduli:

Ordinary moduli:

: 

Large volume modulus with local GUT: Conlon & Quevedo (2007)

: 

Such heavy volume modulus is hard to be compatible with TeV scale SUSY

in the visible sector.

Constraints on large volume modulus density:

Compare with


Thermal Inflation density:

In case that there is any moduli with , thermal inflation is the most

compelling solution to the cosmological moduli problem. Lyth & Stewart (1995)

Most attractive theoretical setup to realize thermal inflation: KC, Chun & Kim(1997)

Models with PQ symmetry spontaneously broken at an intermediate scale by

an interplay between SUSY breaking effect and Planck-scale suppressed effect

T > msoft

V0 ~ msoft2 vPQ2 T = 0

|X| = PQ-breaking flaton

PQ phase transition takes place at T ~ msoft.

 For msoft < T < V01/4, vacuum energy dominates, so there is an inflation with

e-folding ~ ln (V01/4 / msoft) ~ 10.

Such a late inflation can dilute all primordial relics including moduli and gravitinos.

However there is a limitation as thermal inflation produces moduli by itself.

More dilution accompanies more moduli production:

* Dilution factor :

* Moduli density produced by thermal inflation :

primordial moduli from big-bang

moduli from thermal inflation

 maximum dilution when

Moduli density diluted by single thermal inflation including moduli and gravitinos.

ordinary moduli large volume modulus

Huge dilution (compare with the undiluted ) ,

however for < 10 GeV, not enough!

Can we make the large volume modulus heavier than 10 GeV, so that single thermal

inflation is enough ?

To determine the large volume modulus mass when msoft = O(1) TeV , we need

information on both “moduli stabilization” and“mediation of SUSY breaking”.

Our example:

Large volume scenario (LVS) involving Balasubramanian,Berglund,Conlon& Quevedo

* Local GUT (or MSSM) on a small visible sector cycle with MGUT ~ 1016 GeV

* PQ sector for thermal inflation & axion solving the strong CP problem

 ,

So in most cases single thermal inflation is not enough to solve the cosmological

moduli problem of the large volume modulus!

We need additional dilution, which can be done by a that single thermalsecond stage of

thermal inflation:

 double thermal inflation

On the other hand, any pre-existing baryon asymmetry is washed away by

thermal inflation, so a successful model of thermal inflation should involve

a mechanism to generate baryon asymmetry after the last thermal inflation:

 Late time Affleck-Dine leptogenesis by LHu flat direction

Stewart, Kawasaki & Yanagida (1996); Jeong, Kadota, Park & Stewart (2004)

Double thermal inflation with AD leptogenesis that single thermalKC, Park & Shin

1)1st thermal inflation by X1(= flaton 1)

2) LHu(= AD flaton) rolls away from the origin for later leptogenesis

3) 2nd thermal inflation by X2(= flaton 2)

4) LHu comes back to the origin with an angular motion

This scenario requires several nontrivial conditions:

* Hierarchical structure in SUSY breaking flaton masses:

* Reheating by decaying X1 is efficient enough to keep X2 at the origin until

the Universe is dominated by the vacuum energy of X2

* ForAD leptogenesis, is generated by the VEV of X2 , so

Dilution of moduli by double thermal inflation that single thermal

Dilution by 1st TI:

Dilution by 2nd TI:

Final moduli density:

Our model for double thermal inflation in LVS that single thermal

= Large volume sector + PQ sector for the 1st TI

+ Additional flaton sector for the 2nd TI + MSSM sector

* Large volume sector: Balasubramanian et al

Large bulk volume VCY = tb3/2 (tb = Tb + Tb*) for MGUT/MPlanck ~ 10-2

and small cycle (ts = Ts + Ts*) supporting instantons

 ,

PQ sector that single thermal

*Visible sector cycle Tv with axionic shift symmetry U(1)T :

* Anomalous U(1)A gauge symmetry with vanishing FI-term:

 1) Stabilize Tv by the D-term potential at high scale ~ Mstring(Blumenhagen et al)

2) Leave a global PQ symmetry as a low energy remnant of U(1)A and U(1)T

3) Break SUSY with (KC, Nilles, Shin, Trapletti)

*U(1)A charged matter fields X1 & Y1

 1) Break the PQ symmetry spontaneously at vPQ ~ ( msoft MGUT )1/2

and provide QCD axion solving the strong CP problem

2) Implement the 1st thermal inflation

3) Break SUSY with which can provide gauge-mediated

soft masses of O(m3/2)

PQ sector that single thermalloop –induced moduli redefinition(Conlon & Pedro)

Axionic shift symmetry:

Anomalous U(1) gauge symmetry:

D-term potential 

SUSY breaking by the massive U(1)A vector multiplet: KC, Nilles, Shin, Trapletti


Stabilization of PQ charged that single thermal(= U(1)A charged) matter fields:

(D-term contribution) (moduli-mediation)

* Arg (X1) = QCD axion with a decay constant vPQ = < X1> ~ (m3/2MGUT)1/2

* |X1| = flaton implementing the 1st thermal inflation

PQ sector provides with additional important source of SUSY breaking!

* Seesaw mechanism for the F-components:

 FY1 can give rise to gauge mediated soft masses ~ O(m3/2) in the MSSM sector

with a messenger scale

Another flaton that single thermal(U(1)A-singlet) sector for 2nd thermal inflation

2nd thermal inflation with AD leptogenesis with

Dark Matter: LSP is the fermionic partner of the 2nd flaton with a mass .

 SUSY events at the LHC can have softer MET or displaced vertex.

SUSY breaking and its mediation: that single thermal

* Moduli sector moduli-mediated soft masses of (= FTv , FTs)

(At tree level, large volume modulus with FTb/tb= m3/2 is sequestered from the visible sector)

*PQ sector with anomalous U(1):

 U(1)A D-term and gauge-mediated soft masses of

1)stabilize the visible sector cycle

2) implement the 1st TI

3) provide QCD axion with an intermediate scale decay constant

The 1st flaton X1 is U(1)A charged, while the 2nd flaton X2 is U(1)A neutral.

mX1 from D-term ~ mLHu from gauge mediation >> mX2 from moduli mediation,

so this multiple mediation of SUSY breaking provides a flaton mass pattern which

can successfully realize double thermal inflation & AD leptogenesis.

After the 2 inflationnd thermal inflation, correct amount of dark matter and

baryon asymmetry can be produced.

dark matter

moduli from NLSP

diluted decay




from AD


Conclusion inflation

1) Local GUT model with a large bulk volume which may explain MGUT/Mplanck ~ 10-2

suffers from a severe cosmological moduli problem which may require

double thermal inflation.

2) LVS with “anomalous U(1)A gauge symmetry and appropriate U(1)A charged

matter fields” provides a natural setup for multiple mediation of SUSY breaking

(U(1)A D-term, gauge & moduli mediations) which gives rise to a flaton mass pattern

required for successful double thermal inflation and AD leptogenesis.

3) This set up gives also the desired QCD axion with an intermediate PQ scale

vPQ ~ ( msoft MGUT )1/2.

4) LSP is a flatino with mass ~ 10 GeV, with which SUSY events at the LHC can

have softer MET or displaced vertex.