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
Cosmological Moduli Problem and DoubleThermal Inflation
in Large Volume Scenario
KC, W.I. Park & C.S. Shin, arXiv:1207.xxxx
String Pheno 2012
(June 25, Cambridge)
* 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
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
* 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:
KC, Chun & Kim (1998)
* 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:
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
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
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”.
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 second stage of
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 KC, 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
Dilution by 1st TI:
Dilution by 2nd TI:
Final moduli density:
Our model for double thermal inflation in LVS
= 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
*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 loop –induced moduli redefinition(Conlon & Pedro)
Axionic shift symmetry:
Anomalous U(1) gauge symmetry:
SUSY breaking by the massive U(1)A vector multiplet: KC, Nilles, Shin, Trapletti
Stabilization of PQ charged (= 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 (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:
* 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.
Volume modulus density diluted by double thermal inflation
KC, Park & Shin
After the 2nd thermal inflation, correct amount of dark matter and
baryon asymmetry can be produced.
moduli from NLSP
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.