1 Circular Polarization of Gravitational Waves in String Cosmology MIAMI, 200 ７ Jiro Soda Kyoto University work with Masaki Satoh & Sugumi Kanno arXiv:

2 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.

3 Circular polarization of GW Left-handed circular polarization Right-handed circular polarization Without a parity violating process, the circular polarization of primordial GW does not exist.

4 Motivation of our work In the effective action of superstring theory, gravitational Chern-Simons term, which violates the parity invariance, often appears. Hence, it may produce Circular polarization of primordial GW Slow roll inflation does not produce circular polarization Gauss-Bonnet term also appears in superstring theory Known result S.Alexander & J.Martin, Phys.Rev.D71, (2005) Our observation We should study the primordial GW in the context of Gauss-Bonnet-Chern-Simons gravity.

5 Summary of our result 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 These effects produce 100 % circular polarization of GW. Moreover, the amplitude is also enhanced by the factor. Hence, the effect is detectable by DECIGO/BBO or even by LISA.

6 Outline of my talk Inflation in Gauss-Bonnet-Chern-Simons Gravity A mechanism to produce circular polarization Two field inflation & detectability Conclusion

7 Inflation in Gauss-Bonnet - Chern-Simons Gravity

8 Cosmological background space-time Homogeneous and isotropic universe Friedman equation Scalar field equation For concreteness, we take a simple model The equations can be cast into the autonomous system There exists a region where super-inflation occurs.

9 Numerical Result Slow roll regime Super-inflation regime GB term drives the super-inflation. It indicates the violation of weak energy condition.

10 Analytic solution in Super-inflation regime In the super-inflationary regime, the system can be well described by Gauss-Bonnet dominant equations expandingdecreasing It is not difficult to obtain an analytic solution What can we expect for the gravitational waves in this background?

11 A mechanism to produce circular polarization

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

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

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

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

16 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.

17 However, we have to consider the scalar curvature perturbations for which we also expect the very blue power spectrum Everything seems to go well. Fortunately, it is possible to circumvent this difficulty.

18 Two field inflation & detectability

19 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!

20 Two-field inflation 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. field drives the first inflation where CMB spectrum is relevant field drives the second inflation where GB and CS are important

21 A concrete realization

22 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

23 Conclusion

24 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!

25 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