The trouble with asymptotically Safe Inflation

1. The trouble withasymptotically Safe Inflation Qing-Guo Huang Based on arXiv: 1210.7596 done with C. Fang USTC-ICTS State Key Laboratory of Theoretical Physics Institute of Theoretical Physics, CAS 03/14/2013

2. Outline • Why inflation? • What is the asymptotically safe inflation? • Curvature perturbation in asymptotically safe inflation • Discussion

3. Why inflation?

7. Hubble，1929

8. BIG BANG

9. 1978, Arno A. Penzias and Robert W. Wilson

10. 2006, G. Smoot and J. Mather

11. WMAP（世界地图）

13. Matter-dominant era: Radiation-dominant era:

15. Inflation

18. Old inflation：

19. Dynamics of slow-roll inflation： Reheating

20. 2011.06.01

21. What is the nature of inflaton? Is there an inflation model without inflaton?

22. What is the asymptotically safe inflation?

23. It is well-known that Einstein gravity involves a dimensionful coupling constant and is not renormalizable. Decades ago Weinberg suggested that the effective quantum theory of gravitation might be asymptotically safe, and hence UV complete. That is, the renormalization group flows might have a fixed point, with a finite-dimensional UV critical surface of trajectories attracted to the fixed point at short distance. S. Weinberg, 1977

24. Asymptotically safe gravity can be naturally applied to explore the physics in the early universe. The beauty of asymptotically safe inflation is that it does not need any inflaton field. S. Weinberg, 2010

25. If ω=0, we obtain a pure de Sitter solution. Inflation must end in our universe. We hope that the term with R2 might introduce an instability around dS solution.

26. instability Re(ξ)>0 ξ+>0 if ω<0. For –κ/ω<<1, Requiring Nt >60 implies κ<-ω/10.

27. Requiring |δH/H|<<1 implies ε/ξ<<1.

28. RG flow s is asymptotically free. ω has a stable fixed point at ω*=-0.0228. Niedermaier, Reuter, 2006

29. RG flow At the fixed point with s=0, ω=ω* Niedermaier, 2009

30. In the IR limit, the Einstein Hilbert term in the action becomes In the UV limit (μ>>μ0), Tye, Xu, 2010

31. Inflation is assumed to be away from the UV fixed point. Tye, Xu, 2010

32. Curvature perturbation

34. Gravitational Waves Perturbation

35. R R2 C2

36. Higher derivative with respect to time implies one more degree of freedom. Lagrange multiplier ghost ghost E.O.M: Conjugate momenta:

40. The canonical quantization conditions: In the sub-horizon limit,

42. Amplitude of gravitational waves perturbation:

43. Scalar Curvature Perturbation

46. Discussion • The instability can come from the term of R2 as long as ω<0. • The asymptotically safe inflation can achieve a large number of e-folds if -κ/ω<0.1. • In this case the asymptotically safe inflation suffers from ghost problem.

48. Thank You!