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Non-BPS D-branes in the Early Universe

Non-BPS D-branes in the Early Universe. JHEP 0603 (2006) 070 (hep-th/0601133) JHEP (2002) 072 (hep-th/0212063) JHEP (2003) 002 (hep-th/0303236) Prog. Theor. Phys. 112 (2004) 653 (hep-th/0403078) Hokkaido Univ. Kenji Hotta. 1. Introduction. Superstring

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Non-BPS D-branes in the Early Universe

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  1. Non-BPS D-branes inthe Early Universe JHEP 0603 (2006) 070 (hep-th/0601133) JHEP (2002) 072 (hep-th/0212063) JHEP (2003) 002 (hep-th/0303236) Prog. Theor. Phys. 112 (2004) 653 (hep-th/0403078) Hokkaido Univ.Kenji Hotta

  2. 1. Introduction • Superstring • 1-dim. extended object in 10-dim. spacetime • Dp-brane(IIA p : even, IIB p : odd) • p-dim. extended object,½ SUSY • hypersurface the ends of • open strings can attach to

  3. Non-BPS Dp-brane, Dp-Dp Pair (non-SUSY) • (IIA p : odd, IIB p : even) • open string tachyon tachyon potential • Sen’s conjecture potential height=brane tension • Tachyon potential of N Non-BPS Dp-branes Based on BSFT (BSFT: boundary string field theory)

  4. Early Universe (high temperature, high density) • finite temperature system of unstable branes • finite temperature effective potential (BSFT) • Non-BPS D9-branes and D9-D9 pairs become stable near the Hagedorn temperature. Hotta • Thermodynamic Balance on Non-BPS D9 • (open string closed string) • Open strings dominate the total energy of strings. • Cosmological Model based on BSFT? • Sen’s Born-Infeld type action • time evolution of universe • in the presence of non-BPS D9-branes brane inflation?

  5. Decent Relation • Non-BPS D9-branes or D9-D9 pairs • tachyon condensation • lower-dim. D-branes as topological defects • ex) D8-brane = kink solution on non-BPS D9-brane • ‘Brane World Formation Scenario’ • formation of our Brane World as a topological defect in a cosmological context • KKLT model, RS model, Brane Gas Cosmology, ekpyrotic universe We study the homogeneous and isotropic tachyon condensation as a first step towards ‘Brane World Formation Scenario’.

  6. Contents • Introduction  • Phase Transition near the Hagedorn Temperature • Thermodynamic Balance on Non-BPS D9-branes • Action • Constant Dilaton Case • Conclusion and Discussion

  7. 2. Phase Transition near the Hagedorn Temperature • Hagedorn Temperature • maximum temperature for perturbative strings • A single energetic string captures most of the energy.

  8. Non-compact Flat Background •  Non-BPS D9-branes • term of finite temperature effective potential • The coefficient vanishes when • Above becomes the potential minimum. • A phase transition occurs at • and non-BPS D9-branes become stable. •  Non-BPS Dp-branes with • No phase transition occurs.

  9. Toroidal Flat Background  Non-BPS Dp-branes are extended in all the non-compact directions. • A phase transition occurs. •  Non-BPS Dp-branes are not extended in all the non-compact directions. • No phase transition occurs. • Dp-Dp Pairs • similar to the non-BPS D-brane case • The spacetime-filling branes are created near the Hagedorn temperature in all the cases.

  10. 3. Thermodynamic Balance on Non-BPS D9-branes • Thermodynamic Balance Condition • open strings • We need an infinite energy to reach the Hagedorn temperature. closed strings • We can reach the Hagedorn temperature by supplying a finite energy. Energy flows from closed strings to open strings. Open strings dominate the total energy

  11. 4. Action • Gravity • IIA SUGRA (closed string tree) • Einstein gravity

  12. Open String Gas (high temperature) • Matsubara Method (open string 1-loop) • eq. of state

  13. Non-BPS D9-brane (zero temperature) • Non-BPS D9-brane action (open string tree) (BSFT)

  14. 5. Constant Dilaton Case • Open String Gas Case • eq. of motion (RW Spatially Flat Metric)

  15. eq. of state • solution • initial singularity deceleration • low rolling tachyon

  16. Rolling Tachyon Case • eq. of motion (RW Spatially Flat Metric) • Independent eqs. are two of three eqs.

  17. Numerical solution • initial condition close to solution • de Sitter solution • de Sitter deceleration • tachyon matter • cf) Sugimoto-Terashima model

  18. 6. Conclusion and Discussion • Time Evolution of the Universe in the Presence of Non-BPS D9-branes • string gas rolling tachyon • Constant Dilaton Case • deceleration inflation deceleration

  19. Interpolation between High Case and Case • tachyon potential at intermediate temperature • Correction • correction, higher-loop correction • ‘Brane World Formation Scenario’ • Non-BPS D9-branes or D9-D9 pairs • tachyon condensation • lower-dim. D-branes as topological defects • Brane World? • inhomogeneous case, arbitrary matrix • Closed String Emission • closed string emission by D-brane decay Lambert-Liu-Maldacena • tachyon matter?

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