1. 1 Circular Polarization of Gravitational Waves in String Cosmology KITPC, 200 ７.11.23 Jiro Soda Kyoto University work with Masaki Satoh & Sugumi Kanno arXiv:0706.3585

2. 2 弦理論的宇宙論 円偏極重力波生成 KITPC, 200 ７年 11 月 23 日 早田 次郎 京都大学理学研究科

3. 3 Why primordial GW? In other words, one can see the very early universe through GW! Of course, due to the weakness of gravity, it would be difficult to see GW. Typically, we need to see a very small number However, it is not impossible thanks to the current technology!! Hence, taking look at the beginning of the universe is exciting and challenging. Because the gravitational interaction is so weak, gravitational waves can propagate freely even from the very early universe. That’s why we are so fascinated by the primordial GW.

4. 4 Plan of the talk Basics of GW Primordial GW generated during slow roll Inflation Inflation in Chern-Simons-Gauss-Bonnet Gravity A mechanism to produce circular polarization of GW Two field model & detectability Conclusion

5. 5 Polarization of Gravitational Waves GW propagating in the z direction can be written in the TT gauge as Action for GW Any linear combination of these polarization can be a basis of GW.

6. 6 Circular polarization Left-handed circular polarization Right-handed circular polarization

7. 7 Astrophysical sources Free fall time scalefrequency Ex. NS binary Ex. White dwarf binary Ex. Giant BH binary LISA range LIGO range Assuming the distance to be 100Mpc, the amplitude is about

8. 8 Cosmological sources The observed frequency is redshifted to EW scale For cosmological source, the typical frequency would be In the thermal case, we have Ex. In the thermal case, we have inflation CMB LISA LIGO Annoying degeneracy

9. 9 How to quantify GW? Energy density of GW LISA BBO at 0.1 Hz Ultimate DECIGO at 0.1 Hz at 1 mHz Let us defineby Density parameter It allows us to compare the amplitude of point sources and cosmological ones. Ex. Detector sensitivity

10. 10 Slow roll inflation Slow roll parameters metric dynamics quasi-deSitter universe slow roll Ex.

11. 11 Origin of fluctuations length t Wavelength of fluctuations Quantum fluctuations A free scalar field Sub-horizon Super-horizon

12. 12 Amplitude of fluctuations curvature perturbations gravitational waves Matching at gives The relationimplies The tensor to the scalar ratio

13. 13 Primordial GW Inflation origin BBN bound CMB bound Pulsar timing (Maggiore 2000) LISA DECIGO/BBO LIGO II There is almost no constraint in this frequency range!

14. 14 Motivation of our work Superstring theory may induceGravitational Chern-Simons term which may produce Circular polarization of GW Slow roll inflation does not produce circular polarization Gauss-Bonnet term is also predicted by superstring theory Known result S.Alexander & J.Martin, Phys.Rev.D71, 063526 (2005) Our observation Then, the purpose of our work is to study the primordial GW in the context of Chern-Simons-Gauss-Bonne gravity.

15. 15 String Inspired Model This term is not relevant to background dynamics, but could produce the circular polarization of gravitational waves Inflaton drives the slow-roll inflation This term induces the super-inflation, and the instability of gravitational waves Combined effect produces the 100 % circular polarization. Moreover, the amplitude is also enhanced by the factor. Hence, the effect is detectable by DECIGO/BBO or even by LISA.

16. 16 Details

17. 17 Cosmological background space-time Homogeneous and isotropic universe This could accelerate the scalar field Friedman equation Scalar field equation This could be dominant For concreteness, we take a simple model

18. 18 Super-inflation regime GB term produces the kinetic energy dominant stage where the system can be well described by expandingdecreasing Thus, GB term drives the super-inflation. It indicates the violation of weak energy condition. It is not difficult to obtain an analytic solution

19. 19 Exit to slow-roll inflationary phase As we will see, subsequently, the slow-roll inflation will commence. At some point, the asymptotic solution ceases to be valid. Fortunately, super-inflation does not continue forever in generic cases. If super-inflation does not end, we encounter the singularity. Exit from the super-inflation can be seen more precisely in the phase diagram.

20. 20 Dynamical Flow in the phase space Using the cosmic time, we have autonomous system Here, H is the physical Hubble.

21. 21 Numerical Result Slow roll regime Super-inflation regime What can we expect for the gravitational waves in this background?

22. 22 Gravitational waves Tensor perturbation Polarization state Circular polarization With the transformation, we get GBCS polarization tensor Right-handed and left-handed waves obey different equations!

23. 23 GW in Super inflationary regime For super-inflationary regime Both GB and CS contribute here Thus, we have and on the scales

24. 24 Instability induces Polarization quantization vacuum fluctuations E.O.M. on sub-horizon scales Left-handed mode is simply oscillating, right handed-mode is exponentially growing

25. 25 Schematic picture of evolution Bunch-Davis vacuum instability freeze right-handed

26. 26 Degree of Polarization The instability continues during The growth factorgives Hence, we have the degree of circular polarization The string theory could produce 100 percent circularly polarized GW! Note that the amplitude is also enhanced by the instability.

27. 27 Two field inflation field drives the first inflation where CMB spectrum is relevant field drives the second inflation where GB and CS are important At the onset of the second inflation, GB term induces the super-inflation In principle, it is possible to observe the circular polarization of GW by LISA, if the onset of the second inflation lies in the appropriate period. The amplitude of GW is enhanced there and the circular polarization is created.

28. 28 A concrete realization

29. 29 Detectability We thus have the following schematic picture. It should be stressed that our model is completely consistent with current observations. Seto 2006 at Assuming 10 years observational time For LIGO and LCGT, we have Taruya&Seto 2007

30. 30 Summary Observe the circular polarization of primordial gravitational waves! It must be easier than that we have thought before. Because the amplitude is enhanced by several orders! It strongly supports the superstring theory. At least, it indicates the existence of gravitational Chen-Simons term. That might be a signature of the superstring theory!