Circular Polarization of Gravitational Waves in String Cosmology

1. KITPC, 200７.11.23 Circular Polarization of Gravitational Waves in String Cosmology Jiro Soda Kyoto University work with Masaki Satoh & Sugumi Kanno arXiv:0706.3585

2. KITPC, 200７年11月23日 　弦理論的宇宙論　円偏極重力波生成 早田　次郎 京都大学理学研究科

3. Why primordial GW? Because the gravitational interaction is so weak, gravitational waves can propagate freely even from the very early universe. 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. That’s why we are so fascinated by the primordial GW.

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

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

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

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

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

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

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

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

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

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

15. String Inspired Model Inflaton drives the slow-roll inflation This term is not relevant to background dynamics, but could produce the circular polarization of gravitational waves 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. Details

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

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

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

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

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

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

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

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

26. Degree of Polarization The instability continues during The growth factor gives 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. 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 The amplitude of GW is enhanced there and the circular polarization is created. 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.

28. A concrete realization

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

30. Summary Observe the circular polarization of primordial gravitational waves! That might be a signature of the superstring theory! 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.