1. Determination of tensor spectral index in the CMB Wen Zhao @ IHEP. 2012

2. Introduction The models of inflation predict the primordial power spectrum of the primordial (relic) gravitational waves. Detection of RGWs provides a chance to study how the Universe was born. The only way to detect very low frequency RGWs is by studying the Cosmic Microwave Background Radiation (CMB). This talk will discuss how well we can determine the RGWs by the CMB observations.

4. The choice of pivot wavenumber

9. Ground-based Experiments Ground-based experiments can well detect the CMB polarization by observing a small part of full sky for a long time. In the near future, there are several ground-based experiments will begin to works, including QUad, BICEP, POLARBERA, QUIET, ClOVER, QUIJOTE, ACTPOL, SPTPOL, QUBIC and so on. The instrumental noises of the experiments in the near future are very close to the cosmic lensing limit. In addition to the space-based Planck satellites and the various ground-based experiments, some balloon-borne experiments (EBEX, PIPER, Spider). They have the similar detection ability as the ground-based experiments.

10. Planck or ground-based experiment?

12. Difference of Planck and Ground-based Experiments If detectable, Planck can only detect the reionization peak at l~6. Ground-based (or balloon-borne) experiments can only detect the recombination peak at l~100. CMBPol will detect both peaks!

13. Planck + PolarBear (WZ & Zhang 2009)

14. Planned CMBPol (COrE, LiteBird) experiment (see CMBPol white book for details) (WZ, 2011)

15. CMBPol ------ instrumental noises + lensing

17. CMBPol ------ foregrounds

19. Ideal CMB experiment Cosmic lensing generates the E-B mixtures, and forms a nearly white B- mode spectrum. For the ideal experiment, where only the reduced cosmic lensing contamination is considered. Detection limit: (WZ & Baskaran 2009)

21. Testing inflationary consistency relations (WZ & Huang, 2011)

22. Single-field slow-roll inflations consistency relation Results: r > 0.14 for EPIC-2m r > 0.06 for Ideal

23. Potential-driven G-inflations

24. Conclusions The CMB observations provide an excellent opportunity to determine the RGWs. We have derived the analytic formulae for: best-pivot wavenumber; signal-to-noise ratio and uncertainty of nt. The uncertainties of r and nt strongly depends on the cosmic reionization, especially for nt. Ignoring the foreground contaminations, Planck: △ nt~0.25 for r=0.1. Ideal: △ nt~0.007 for r=0.1 The inflationary consistency relations are quite difficult to be tested.

25. Thank you!