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

Outline 1) Introduction * Local GUT in large bulk volume which is responsible for M GUT /M Planck ~ * 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

Introduction One of the most attractive features of TeV scale SUSY is the successful unification of gauge couplings at M GUT ~ GeV. On the other hand, this value of M GUT is meaningfully lower than M Planck ~ GeV, which might require an explanation. One possible explanation : Gravity in large bulk space and local GUT on branes (at boundary or small cycle) Horava & Witten, … 

In 4D effective theory, the scale hierarchy M GUT /M Planck ~ 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.  10 4

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: * 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 Compare with ㅏㅏㅏ

Thermal Inflation 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 > m soft V 0 ~ m soft 2 v PQ 2 T = 0 |X| = PQ-breaking flaton PQ phase transition takes place at T ~ m soft.  For m soft < T < V 0 1/4, vacuum energy dominates, so there is an inflation with e-folding ~ ln (V 0 1/4 / m soft ) ~ 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 m soft = 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 M GUT ~ 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 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 LH u flat direction Stewart, Kawasaki & Yanagida (1996); Jeong, Kadota, Park & Stewart (2004)

Double thermal inflation with AD leptogenesis KC, Park & Shin 1) 1 st thermal inflation by X 1 (= flaton 1) 2) LH u (= AD flaton) rolls away from the origin for later leptogenesis 3) 2 nd thermal inflation by X 2 (= flaton 2) 4) LH u 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 X 1 is efficient enough to keep X 2 at the origin until the Universe is dominated by the vacuum energy of X 2  * For AD leptogenesis, is generated by the VEV of X 2, so

Dilution of moduli by double thermal inflation Dilution by 1 st TI: Dilution by 2 nd TI: Final moduli density:

Our model for double thermal inflation in LVS = Large volume sector + PQ sector for the 1 st TI + Additional flaton sector for the 2 nd TI + MSSM sector * Large volume sector: Balasubramanian et al Large bulk volume V CY = t b 3/2 (t b = T b + T b *) for M GUT /M Planck ~ and small cycle (t s = T s + T s *) supporting instantons ,

PQ sector * Visible sector cycle T v with axionic shift symmetry U(1) T : * Anomalous U(1) A gauge symmetry with vanishing FI-term:  1) Stabilize T v by the D-term potential at high scale ~ M string (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 X 1 & Y 1  1) Break the PQ symmetry spontaneously at v PQ ~ ( m soft M GUT ) 1/2 and provide QCD axion solving the strong CP problem 2) Implement the 1 st thermal inflation 3) Break SUSY with which can provide gauge-mediated soft masses of O(m 3/2 )

PQ sector loop –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 (= U(1) A charged) matter fields: (D-term contribution) (moduli-mediation)  * Arg (X 1 ) = QCD axion with a decay constant v PQ = ~ (m 3/2 M GUT ) 1/2 * |X 1 | = flaton implementing the 1 st thermal inflation PQ sector provides with additional important source of SUSY breaking! * Seesaw mechanism for the F-components:  F Y1 can give rise to gauge mediated soft masses ~ O(m 3/2 ) in the MSSM sector with a messenger scale

Another flaton (U(1) A -singlet) sector for 2 nd thermal inflation 2 nd thermal inflation with AD leptogenesis with Dark Matter: LSP is the fermionic partner of the 2 nd 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 (= F Tv, F Ts ) (At tree level, large volume modulus with F Tb / t b = m 3/2 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 1 st TI 3) provide QCD axion with an intermediate scale decay constant The 1 st flaton X 1 is U(1) A charged, while the 2 nd flaton X 2 is U(1) A neutral.  m X1 from D-term ~ m LHu from gauge mediation >> m X2 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 2 nd thermal inflation, correct amount of dark matter and baryon asymmetry can be produced. dark matter moduli from NLSP diluted decay enough baryon asymmetry from AD leptogenesis

Conclusion 1) Local GUT model with a large bulk volume which may explain M GUT /M planck ~ 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 v PQ ~ ( m soft M GUT ) 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.