Collaboration : M. Sakellariadou, R. Jeannerot.

References : Jeannerot, J. R., Sakellariadou (2003) [PRD 68, 103514]

J. R., M. Sakellariadou (2005) [PRL 94, JCAP 0503]

by

Jonathan RocherJonathan Rocher, GRCO – IAP, France

Thursday 21 july 2005

EINSTEIN century Meeting 2005

I. Genericity of cosmic string formation in SUSY GUTsI. Genericity of cosmic string formation in SUSY GUTs Ingredients of SUSY GUTsIngredients of SUSY GUTs Formation of topological defectsFormation of topological defects

II. Constraints on inflationary modelsII. Constraints on inflationary models Inflationary contribution to the CMB anisotropiesInflationary contribution to the CMB anisotropies Cosmic strings contribution to the CMB anisotropiesCosmic strings contribution to the CMB anisotropies Constraining F-term inflation Constraining F-term inflation Constraining D-term inflation Constraining D-term inflation

ConclusionsConclusions

I.I.

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 : ~ M2infl

ARE THEY CONSISTENT WTH CMB DATA ?

WHAT IS THEIR CONTRIBUTION TO THE CMB ANISOTROPIES ?

SO(10) 4C 2L 2R

3C 2L 2R 1B-L

3C 2L 1R 1B-L

3C 2L 1R 1B-L

GSM Z2

GSM Z2

GSM Z2

GSM Z2

GSM Z2

GSM Z2

4C 2L 1R

3C 2L 1R 1B-L

11 11 22

22

22

22

11

2211

11

11

? GUT

InflationStandard Model

time

11: Monopoles 22: Cosmic Strings INFLATION

II. II.

II.1II.1

)( 2MSW F Superpotential for F-term inflation :

termsDSMSV F 2222222),,(

[Dvali, Shafi, Schaefer PRL73 (1994)]

A local minimum for S>>SC, <+>=<->=0,

VV0 0 = = 22 MM 44 Perfectly flat direction

+ SUSY breaking

=> 1-loop radiative corrections[Coleman and Weinberg, PRD7 (1973)]

NMSVMSV ,/1 )( 2242eff

where S : Inflaton, + - : pair of Higgs in non trivial representation of G

12

2P

2

scal

)(

QQQQ

Q

xfyxM

M

N

N

T

T [Senoguz and Shafi, PLB567 (2003)]

where xQ=SQ/M ,

and yQ and f are functions of xQ.

Assuming V<<V0, and using the complete effective potential for V’(|S|),

2P

2

tens M

M

T

T

Q

II.2II.2The cosmic strings contribution is proportionnal to the mass per unit lenght In this model (for Nambu-Goto strings),

2P

2

strings

and M

M

T

TM

Q

In addition we require NQ=60. This provide a relation between M and xQ.

Only 1 unknown xQ.

In conclusion, three sources contribute to the CMB quadrupole anisotropy :

strings

2

tens

2

scal

2

tot

2

QQQQT

T

T

T

T

T

T

T

with 1 unknown (xQ) for a given value of and N (SO(10) gives N=126).

• The r.h.s. is normalised to COBE (T/T)Q ~ 6×10-6.

• Thus we obtain xQ() and thus M(). We can calculate the strings contribution for a given defining

tot

2

strings

2

QQCS T

TTT

II.3 II.3 --

• Gravitino constraint on the reheating temperature impose < 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), < 7×10-7 fine tuning (NEW !)

M < 2×1015 GeV

SW D 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 ]

222

SK

II.4II.4--

• 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 !)

GeV 102

103

102

15

5

2

g

WMAP

Fine tuning (NEW !)

Same limit as F-term inflation

• 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 GGUT.

J. Rocher, M. Sakellariadou (2005) [PRL 94, JCAP 0503]

III. III. ::

24

2

2

curvaton

2

init

Pl

Plinit

initQ

M

M

M

T

T

We get an additional

contribution

Conclusion : It is possible for to reach non fine tuned values (10-3).

init can be constrained : GeV

10105

213

init

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>>SC, +=0=-, V0= g2 2/2 and a global minimum for +=0, -=√.

Perfectly flat direction + D-term SUSY breaking => mass siplitting of components of . Including the 1-loop radiative corrections,

SW D Superpotential :

2222

22222

2),,(

gSSV D

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.

SUSY

)1ln()1()1ln()1(ln2

161

2)( 1212

2

22

2

222

eff zzzzSgg

SV

22

22

xg

Sz

The inflaton field reaches MP !! We need SUGRA...

A local minimum for S>>SC, +=0=-, V0= g2 2/2 and a global minimum for +=0=S, -=√.

Perfectly flat direction + D-term SUSY breaking => mass splitting of components of :

SW D Superpotential :

222

22

4242422

23

111 Exp

gS

SSSKV DSUGRA

Minimal Kähler potential and minimal gauge kinetic function f()=1.

222

SK

[Binétruy and Dvali, PLB388 (1996)]

2222

fermion2

22222bosons

2

ExpS

ExpS

P

P

MSm

gMSm

)1ln()1()1ln()1(

Expln2

161

2)( 1212

2

2222

2

222

eff zzzzMSSgg

SV p

22

2222 Expx

g

MSSz p

We obtain a slightly more complicated potential

Completely numerical resolution for a given value of g :

• numerical relation between and xQ thanks to NQ.

• numerical resolution of the nomalisation to COBE :

strings

2

infl

2

COBE

2

QQQT

T

T

T

T

T

C()

xQ