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Constraining SUSY GUTs and Inflation with Cosmology

EINSTEIN century Meeting 2005. Thursday 21 july 2005. Constraining SUSY GUTs and Inflation with Cosmology. by Jonathan Rocher , GR e CO – IAP, France. Collaboration : M. Sakellariadou, R. Jeannerot. References : Jeannerot, J. R., Sakellariadou (2003) [PRD 68 , 103514]

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Constraining SUSY GUTs and Inflation with Cosmology

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  1. EINSTEIN century Meeting 2005 Thursday 21 july 2005 ConstrainingSUSY GUTs and Inflation with Cosmology by Jonathan Rocher, GReCO – IAP, France Collaboration : M. Sakellariadou, R. Jeannerot. References : Jeannerot, J. R., Sakellariadou (2003) [PRD 68, 103514] J. R., M. Sakellariadou (2005) [PRL 94, JCAP 0503]

  2. Outline • I. Genericity of cosmic string formation in SUSY GUTs • Ingredients of SUSY GUTs • Formation of topological defects • II. Constraints on inflationary models • Inflationary contribution to the CMB anisotropies • Cosmic strings contribution to the CMB anisotropies • Constraining F-term inflation • Constraining D-term inflation • Conclusions

  3. I. Genericity of cosmic string formation in SUSY GUTs

  4. Framework = Supersymmetric Grand Unified Theories GUT SSBs + phase transitions Topological defects. • Selection of SSB patterns of GUT groups down to the SM in agreement with : • Particle physics (neutrino oscillation, proton lifetime, SM) • Cosmology (CMB observations, monopole problem, matter/antimatter asymmetry) Ingredients : see-saw mechanism, R-parity, baryogenesis via leptogenesis , … AND a phase of inflation after the formation of monopoles. Most natural in SUSY GUTs : Supersymmetric Hybrid Inflation. It couples the inflaton with a pair of GUT Higgs fields. It ends with a phase transition.

  5. Standard Model ? Inflation GUT time 3C 2L 1R 1B-L GSM Z2 3C 2L 2R 1B-L GSM Z2 GSM Z2 3C 2L 1R 1B-L 4C 2L 1R SO(10) 4C 2L 2R GSM Z2 3C 2L 1R 1B-L GSM Z2 GSM Z2 1 2 1 2 2 1 1 2 1 2 1 INFLATION 1: Monopoles 2: Cosmic Strings • Idem for SO(10), SU(5), SU(6), SU(7), E6, ... • Conclusions : • In SUSY GUTs, formation of cosmic strings = GENERIC (NEW !) • Formation at the end of inflation : m ~ M2infl • ARE THEY CONSISTENT WTH CMB DATA ? • WHAT IS THEIR CONTRIBUTION TO THE CMB ANISOTROPIES ?

  6. II. Constraints on inflationary models

  7. II.1 Inflationary Contribution to CMB anisotropies Superpotential for F-term inflation : where S : Inflaton, F+F- : pair of Higgs in non trivial representation of G [Dvali, Shafi, Schaefer PRL73 (1994)] A local minimum for S>>SC, <f+>=<f->=0, V0 = k2M4 Perfectly flat direction + SUSY breaking => 1-loop radiative corrections [Coleman and Weinberg, PRD7 (1973)]

  8. Assuming DV<<V0, and using the complete effective potential for V’(|S|), [Senoguz and Shafi, PLB567 (2003)] where xQ=SQ/M , and yQ and f are functions of xQ. In addition we require NQ=60. This provide a relation between M and xQ. Only 1 unknown xQ. II.2 Cosmic strings contribution to CMB anisotropies The cosmic strings contribution is proportionnal to the mass per unit lenght m . In this model (for Nambu-Goto strings),

  9. Total contribution to CMB anisotropies In conclusion, three sources contribute to the CMB quadrupole anisotropy : • with 1 unknown (xQ) for a given value of k and N (SO(10) gives N=126). • The r.h.s. is normalised to COBE (dT/T)Q ~ 6×10-6. • Thus we obtain xQ(k) and thus M(k). We can calculate the strings contribution for a given k defining

  10. II.3 Constraints on F-term inflation k k • Gravitino constraint on the reheating temperature impose k< 8×10-3 • In WMAP, the cosmic strings contribution to the CMB anisotropies is lower than 10% (99% CL). [Pogosian et al. JCAP 0409 (2004)] • Conclusion : for SO(10), k < 7×10-7 fine tuning (NEW !) • M < 2×1015 GeV

  11. II.4 Constraints on D-term inflation Introduction of an additionnal U(1) factor with a gauge coupling g and a non vanishing FI term x. [ Charges under U(1) : Q(F±)=±1, Q(S)=0 ] • Superpotential : • In the SUSY framework : the inflaton field reaches the PLANCK mass!! • Supergravity is needed. Study in the minimal supergravity : Completely numerical resolution. We obtain the cosmic strings contribution as a function of the 3 parameters : g, l, √x .

  12. WMAP • The WMAP constraint on cosmic string contribution to the CMB imposes • The SUGRA corrections induce a lower limit on l ! • The D-term inflation is still an open possibility (NEW !) Fine tuning (NEW !) Same limit as F-term inflation

  13. Conclusions • Formation of cosmic strings is very GENERIC within SUSY GUTs. • GUTcosmic strings are compatible with current CMB measurements. • Their low influence on the power spectrum can be used to constraininflationary models • For F-term inflation, both the superpotential coupling k and the mass scale M can be constrained. • For D-term inflation, the gauge g and the superpotential l coupling constant as well as the FI term x are constrained. • The SUGRA framework is necessary. This is still an open possibility. • These models suffer from some fine tuning except with a curvaton. • Measuring the strings contribution can allow to discriminate between different N and thus different GGUT. • J. Rocher, M. Sakellariadou (2005) [PRL 94, JCAP 0503]

  14. III. To avoid fine tuning: Curvaton mecanism

  15. Let’s consider that the inflaton field drive the expansion of the universe while an additional scalar field ygenerates the primordial fluctuations. We get an additional contribution Conclusion : It is possible for k to reach non fine tuned values (10-3). yinit can be constrained :

  16. The D-term inflation Introduction of an additionnal U(1) factor with a gauge coupling g and a non vanishing FI term x. Charges under U(1) : Q(F±)=±1, Q(S)=0. Superpotential : SUSY A local minimum for S>>SC, f+=0=f-, V0= g2 x2/2and a global minimum for f+=0, f-=√x. Perfectly flat direction + D-term SUSY breaking => mass siplitting of components of F. Including the 1-loop radiative corrections, The inflaton field reaches MP !! We need SUGRA...

  17. The D-term inflation in supergravity : Superpotential : Minimal Kähler potential and minimal gauge kinetic function f(F)=1. SUGRA [Binétruy and Dvali, PLB388 (1996)] A local minimum for S>>SC, f+=0=f-, V0= g2 x2/2and a global minimum for f+=0=S, f-=√x. Perfectly flat direction + D-term SUSY breaking => mass splitting of components of F :

  18. C(x) xQ We obtain a slightly more complicated potential • Completely numerical resolution for a given value of g : • numerical relation between x and xQ thanks to NQ. • numerical resolution of the nomalisation to COBE :

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