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

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

I. Genericity of cosmic string formation in SUSY GUTs

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.

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 2 infl ARE THEY CONSISTENT WTH CMB DATA ? WHAT IS THEIR CONTRIBUTION TO THE CMB ANISOTROPIES ? SO(10) 4 C 2 L 2 R 3 C 2 L 2 R 1 B-L 3 C 2 L 1 R 1 B-L G SM Z 2 4 C 2 L 1 R 3 C 2 L 1 R 1 B-L ? GUT Inflation Standard Model time 12 1: Monopoles 2: Cosmic Strings INFLATION

II. Constraints on inflationary models

II.1 Inflationary Contribution to CMB anisotropies Superpotential for F-term inflation : [Dvali, Shafi, Schaefer PRL73 (1994)] A local minimum for S>>S C, = =0, V 0 =   2 M 4 V 0 =   2 M 4 Perfectly flat direction + SUSY breaking => 1-loop radiative corrections [Coleman and Weinberg, PRD7 (1973)] where S : Inflaton,  +  - : pair of Higgs in non trivial representation of G

[Senoguz and Shafi, PLB567 (2003)] where x Q =S Q /M, and y Q and f are functions of x Q. Assuming  V<<V 0, and using the complete effective potential for V’(|S|), II.2 Cosmic strings contribution to CMB anisotropies The cosmic strings contribution is proportionnal to the mass per unit lenght  In this model (for Nambu-Goto strings), In addition we require N Q =60. This provide a relation between M and x Q. Only 1 unknown x Q.

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

II.3 Constraints on F - term inflation Gravitino constraint on the reheating temperature impose  < 8 × 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),  < 7 × fine tuning (NEW !) M < 2 × GeV 

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,, √  Introduction of an additionnal U(1) factor with a gauge coupling g and a non vanishing FI term . [ Charges under U(1) : Q(  ± )=±1, Q(S)=0 ] II.4 Constraints on D - term inflation

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

Conclusions Formation of cosmic strings is very GENERIC within SUSY GUTs. GUT cosmic strings are compatible with current CMB measurements. Their low influence on the power spectrum can be used to constrain inflationary models For F-term inflation, both the superpotential coupling  and the mass scale M can be constrained. For D-term inflation, the gauge g and the superpotential coupling constant as well as the FI term  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 G GUT. J. Rocher, M. Sakellariadou (2005) [PRL 94, JCAP 0503]

III. To avoid fine tuning : Curvaton mecanism

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

A local minimum for S>>S C,  + =0=  -, V 0 = g 2  2 /2 and a g lobal minimum for  + =0,  - =√ . Perfectly flat direction + D-term SUSY breaking => mass siplitting of components of . Including the 1-loop radiative corrections, D-term The D-term inflation Superpotential : Introduction of an additionnal U(1) factor with a gauge coupling g and a non vanishing FI term . Charges under U(1) : Q(  ± )=±1, Q(S)=0. SUSYSUSY The inflaton field reaches M P !! We need SUGRA...

A local minimum for S>>S C,  + =0=  -, V 0 = g 2  2 /2 and a g lobal minimum for  + =0=S,  - =√ . Perfectly flat direction + D-term SUSY breaking => mass splitting of components of  : D-term The D-term inflation in supergravity : Superpotential : SUGRASUGRA Minimal Kähler potential and minimal gauge kinetic function f(  )=1. [Binétruy and Dvali, PLB388 (1996)]

We obtain a slightly more complicated potential Completely numerical resolution for a given value of g : numerical relation between  and x Q thanks to N Q. numerical resolution of the nomalisation to COBE : C(  ) xQxQ