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

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HEP /04/2006 V. Zamarias2 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.

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HEP /04/2006 V. Zamarias3 1. Type-0 String Backgound Action: Φ: Dilaton field. T bulk : Bulk (closed) Tachyon Field F 5 =dC 4 : 5-form field strength of RR field.

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HEP /04/2006 V. Zamarias4 If Φ=Φ 0 =cte and T bulk =cte, for D3-brane Background the metric is: where:

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HEP /04/2006 V. Zamarias5 2. Probe D3-Brane moving in the background of D3-Brane with a Bulk Tachyon field DBI + WZ Action: Mirage Formalism + Type-0 background:

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HEP /04/2006 V. Zamarias6 DBI + WZ Action: with: PARAMETRIZATION:

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HEP /04/2006 V. Zamarias7 3. Geometric Open Tachyon Interpretation with: We introduce a radial coordinate r and we consider only radial movement of the probe Brane.

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HEP /04/2006 V. Zamarias8 and

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HEP /04/2006 V. Zamarias9 4. Coupling to Gravity - Tachyon Cosmology As the Brane moves in the Type-0 String Background it feels 2 effects: a)Its own gravitational field by introducing a curvature term R: Gravitational field on the Brane Open tachyon techniques. b)The gravitational field of the bulk: Mirage Cosmology.

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HEP /04/2006 V. Zamarias10 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:

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HEP /04/2006 V. Zamarias11 We assume a Flat Robertson-Walker metric on the brane

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HEP /04/2006 V. Zamarias12 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:

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HEP /04/2006 V. Zamarias13 We can also calculate the Raychaudhury equation and the inflation parameter: which is a function of the radial distance r and the value of T Bulk. We assume a smooth function: where ζ controls how steep is the variation, while σ indicates when the transition from to occurs.

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HEP /04/2006 V. Zamarias14 E small, ζ = 8, σ = 1.28

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HEP /04/2006 V. Zamarias15 CONCLUSIONS The presence of T Bulk 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 T Bulk and the relation between open and closed strings.

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HEP /04/2006 V. Zamarias16 E small, ζ = 8, σ = 1.28

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HEP /04/2006 V. Zamarias17 OUTLINE Introduction 1.The Bulk: Type-0 String Theory 2.D3-Brane Moving in the Background of D3-Branes with a Bulk Tachyon Field 3.Geometrical Tachyon Dynamics 4.Cosmology Conclusions

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HEP /04/2006 V. Zamarias18 4. Late Time Acceleration ( ) Effective Gravitational Constant: Effective Cosmological Constant: at late time: + Case1 < 3ν < 2,2 - Case0 < 3ν < 1

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