1. 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/0205042 hep-th/02xxxx with S. de Alwis and E. Novak PRL 87 (2001), hep-th/0106174 PRD 64 (2001), hep-th/0002087 with S. de Alwis Inflationary cosmology in the central region of string/M-theory moduli Space

2. String Moduli Space HO I IIB IIA HW MS1 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 TS Central region “minimal computability” Outer region perturbative

3. 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:

4. Scales & Shape of Moduli Potential The width of the central region In effective 4D theory: moduli kinetic terms multiplied by M S 8 V 6 (M 11 9 V 7 in M-theory). Curvature term multiplied by same factors “Calibrate” using 4D Newton’s constant 8  G N =m p -2  Typical distances are order one in units of m p

5. The scale of the potential Numerical examples: NO VOLUME FACTORS!!! Banks

6. The shape of the potential  m p outer region -4-2024 2 V(  M S 6 m p -2 outer region central region zero CC min. & potential vanishes @ infinity  intermediate max.

7. Inflation: constraints & predictions Topological inflation outer region -4-2024 2  m p V(  M S 6 m p -2 outer region central region  – wall thickness in space   Inflation   H > 1   > m p H 2 ~ 1/3    m p 2 

8. Sufficient inflation Slow-roll parameters Number of efolds The “small” parameter Sufficient inflation Quantum fluct. not too large

9. CMB anisotropies and the string scale For consistency need V’’~1/25

10.  1/3 < 25V’’ < 3  For our model If consistent:

11. 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