אוניברסיטת בן-גוריון

Ram Brustein

Outer region of moduli space: problems! Central region: parametrization with N=1 SUGRA Scales & shape of central region potential Inflation: constraints & predictions

hep-th/0205042hep-th/02xxxx

with S. de Alwis and E. NovakPRL 87 (2001), hep-th/0106174PRD 64 (2001), hep-th/0002087

with S. de Alwis

Inflationary cosmology in the

central region of string/M-theory moduli Space

String Moduli Space

HO

IIIB

IIA

HWMS1 HE

Perturbative theories = cosmological disaster

• massless moduli

•Gravity = Einstein’s

•Inflation blocked

Requirements•D=4•N=1 SUSY N=0•CC<(m 3/2)4

•SM (will not discuss)•Volume/Coupling moduli T S

Central region“minimal computability”

Outer regionperturbative

Central Region

• Parametrization with D=4, N=1 SUGRA

• Stabilization by SNP effects @ string scale

• Continuously adjustable parameter

• SUSY breaking @ lower scale by FT effects

• PCCP o.k after SUSY breaking

Our proposal:

Scales & Shape of Moduli Potential

• The width of the central region

In effective 4D theory:

moduli kinetic terms multiplied by MS8 V6 (M11

9 V7 in M-theory).

Curvature term multiplied by same factors“Calibrate” using 4D Newton’s constant 8GN=mp

-2

22421

pp mRgmxd

Typical distances are order one in units of mp

• The scale of the potential

)/(

)(

4214

42214

p

p

mVxd

Vmxd

4263 / pSS mMVMW

Numerical examples:

4/34/3

25/116106.8 gGeV YM

I

2/36/16

4/1

25/116 )4(106.7

VMGeV GUTHWYM

NO VOLUME FACTORS!!!Banks

• The shape of the potential

mp

outer region

-4 -2 0 2 4

2

-1

V(MS6mp

-2

outer regioncentral region

zero CC min. & potential vanishes @ infinity intermediate max.

Inflation: constraints & predictions

• Topological inflation

outer region

-4 -2 0 2 4

2

-1

mp

V(MS6mp

-2

outer regioncentral region

– wall thickness in spaceInflation H > 1 > mp

H2~1/3 mp2

•Sufficient inflation

dN

end

pmend )(

121),(

)(''~,2~ max2

max4

2

Vmp

|(''|

22

max)

2

V

mp

Slow-roll parameters

Number of efolds

The “small” parameter

Sufficient inflation 2max )/(120 pinit mExp

6/1)('' max2max VHinit Quantum fluct. not too large

50),( endCMBN 2max )/(100 pCMB mExp

215

'1

232/1 2/3

3 VV

mpP 2

3

2

232/1 )/(100 p

p

mExpm

P

)(''252/)(''105.6 max4/1

max162 VExpVGeV

•CMB anisotropies and the string scale

22/1

3423 )/(100/

3

p

m

pS mExpPmM p

For consistency need V’’~1/25

0

)1)(''25(08.92. max

r

VnS CMB

CMBCMBS

r

n

7.13

241

1/3 < 25V’’ < 3 0

97.76.

rnS

)(''

0~)/'(

max

2

V

VV

CMB

CMB

For our model

If consistent:

)1(6/11

3/1

10

17 325

4

2/1

)(107.1 S

S

nn

P

S eGeVM

Summary and prospects

• Scenario: Stabilization in Central region

• Consistent cosmology: – scaling arguments– Curvature of potential needs to be “smallish”

• Predictions for CMB

Calculate ? possible to some extent