Geometrical Tachyon Dynamics in the Background of a Bulk Tachyon Field

1. Geometrical Tachyon Dynamics in the Background of a Bulk Tachyon Field HEP2006 Recent Developments in High Energy Physics and Cosmology Ioannina - GREECE ZAMARIAS Vassilis In collaboration with E. PAPANTONOPOULOS and Ioanna PAPPA (hep-th 0601152) NTUAthens 15/04/2006

2. Introduction - Motivation • Bulk: Type-0 String background which includes RR fluxes + bulk tachyon field. Effect on the Brane? • Brane: Probe D3-Brane, DBI action + WZ action • Dynamics: Movement of the Probe D3-Brane in the Type-0 background: Mirage Cosmology [A. Kehagias & E. Kiritsis - JHEP 9911, 022 (1999)] • Geometric Open Tachyon Interpretation: Open Tachyon field on the brane rolling down its potential. • Cosmology? Coupling to gravity. V. Zamarias

3. 1. Type-0 String Backgound Action: Φ: Dilaton field. Tbulk: Bulk (closed) Tachyon Field F5=dC4: 5-form field strength of RR field. V. Zamarias

4. If Φ=Φ0=cteand Tbulk=cte, for D3-brane Background the metric is: where: V. Zamarias

5. 2. Probe D3-Brane moving in the background of D3-Brane with a Bulk Tachyon field DBI + WZ Action: • Mirage Formalism + Type-0 background: V. Zamarias

6. DBI + WZ Action: with: • PARAMETRIZATION: V. Zamarias

7. 3. Geometric Open Tachyon Interpretation with: We introduce a radial coordinate r and we consider only radial movement of the probe Brane. V. Zamarias

8. and V. Zamarias

9. 4. Coupling to Gravity - Tachyon Cosmology As the Brane moves in the Type-0 String Background it feels 2 effects: • Its own gravitational field by introducing a curvature term R: Gravitational field on the Brane  Open tachyon techniques. • The gravitational field of the bulk:  Mirage Cosmology. V. Zamarias

10. a. Gravitational Field on the Brane DBI action of the Geometrical Tachyon field coupled to gravity which acts as LOCAL matter source on the brane: Energy-momentum tensor: V. Zamarias

11.  We assume a Flat Robertson-Walker metric on the brane  V. Zamarias

12. b. Gravitational Field of the Bulk As the Brane moves in the Type-0 String Background a metric is induced on the brane (Mirage Cosmology): with η the cosmic time: Defining as a scale factor a=g we get: V. Zamarias

13.  We can also calculate the Raychaudhury equation and the inflation parameter: which is a function of the radial distance r and the value of TBulk. We assume a smooth function: where ζ controls how steep is the variation, while σindicates when the transition from to occurs. V. Zamarias

14. E small, ζ = 8, σ = 1.28 V. Zamarias

15. CONCLUSIONS • The presence of TBulk affects significantly the behavior of the geometrical tachyon field. • We get early inflation with exit from it and late time acceleration without the need of dark energy. • Need of a better understanding of the behavior of the TBulk and the relation between open and closed strings. V. Zamarias

16. E small, ζ = 8, σ = 1.28 V. Zamarias

17. OUTLINE • Introduction • The Bulk: Type-0 String Theory • D3-Brane Moving in the Background of D3-Branes with a Bulk Tachyon Field • Geometrical Tachyon Dynamics • Cosmology • Conclusions V. Zamarias

18. 4. Late Time Acceleration( ) Effective Gravitational Constant: Effective Cosmological Constant: at late time: V. Zamarias