1. Inflationary Attractor Zong-Kuan Guo (advisor: Yuan-Zhong Zhang) Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100080, P.R.China

2. Background Standard Cosmology Inflationary Cosmology Initial Conditions for inflation

3. Outline Inflationary Cosmology Tachyon Cosmology Inflationary Attractor from Tachyonic Matter Braneworld Cosmology Inflationary Attractor in Braneworld Scenario Conclusions

4. Inflationary Cosmology the Einstein-Hilbert action the Friedmann equation the equation of motion of the inflation field the energy density and pressure of a scalar field the conditon for inflation

5. Tachyon Cosmology the effective action of the tachyon field in the Born-Infeld form the Friedmann equation the evolution equation of the tachyon field the energy density and pressure of a tachyon field the condition for inflation

6. Inflationary Attractor from Tachyonic Matter Demonstrate: the Hamilton-Jacobi equations Consider a linear perturbation

7. Analysis: Potential the low-roll curve the potential-dominated region P the kinetic-energy-dominated region K

8. Sketch of the different regions in the phase plane.

9. Phase portrait for the tachyon field with in the standard cosmology.

10. Phase portrait for the tachyon field with in the standard cosmology.

11. Braneworld Cosmology the action in the Randall-Sundrum II model the four-dimensional Einstein equations induced on the brane the modified Friedmann equation on the brane

12. Inflationary Attractor in Braneworld Scenario For a standard inflation, the evolution equation of the field and the modified Friedmann equation the Hamilton-Jacobi equations Consider a linear perturbation

13. Phase portrait for the scalar field with in the braneworld scenario.

14. Phase portrait for the scalar field with in the braneworld scenario.

15. Inflationary Attractor in Braneworld Scenario For a tachyon field, the evolution equation of the field and the modified Friedmann equation the Hamilton-Jacobi equations Consider a linear perturbation

16. Phase portrait for the tachyon field with in the braneworld scenario.

17. Phase portrait for the tachyon field with in the braneworld scenario.

18. Conclusions Tachyon inflation possesses the attractor behavior in the standard cosmology. Inflations driven by a scalar field or a tachyon field in the braneworld scenario possess the attractor behavior. Initial kinetic terms decays more rapidly in the braneworld scenario than in the standard cosmology.

19. Thank you! Thank Yuan-Zhong Zhang, Rong-Gen Cai, Yun-Song Piao, Qing- Guo Huang, Hong-Sheng Zhang, Qi Guo and Xiu-Lian Wang for helpful discussions!