1. 1 COSMIC POLARIZATION ROTATION & COSMOLOGICAL MODELS AND Detectability of Primordial G-Waves Wei-Tou Ni Center for Gravitation and Cosmology, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing, CHINA National Astronomical Observatories, Chinese Academy of Sciences, Beijing, CHINA

2. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 2 CMB Polarization Observation In 2002, DASI microwave interferometer observed the polarization of the cosmic background. With the pseudoscalar-photon interaction, the polarization anisotropy is shifted relative to the temperature anisotropy. In 2003, WMAP found that the polarization and temperature are correlated to 10σ. This gives a constraint of 10 -1 rad or 6 degrees of the cosmic polarization rotation angleΔφ.

3. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 3 CMB Polarization Observation In 2005, the DASI results were extended (Leitch et al.) and observed by CBI (Readhead et al.) and CAPMAP (Barkats et al.) In 2006, BOOMERANG CMB Polarization DASI, CBI, and BOOMERANG detections of Temperature-polarization cross correllation Planck Surveyor will be launched next year with better polarization-temperature measurement and will give a sensitivity to cosmic polarization rotation Δφ of 10 -2 -10 -3.

4. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 4 WMAP 3 year Polarization Maps TT TE EE BB(r=0.3) BB(lensing) foreground

5. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 5 Pseudo-scalars: Pseudoscalar-Photon Coupling

6. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 6 ≈ ξφ, μ A ν F ~μ ν ≈ ξ (1/2)φ F μ ν F ~μ ν (Mod Divergence)

7. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 7 Change of Polarization due to Cosmic Propagation The effect of φ in (2) is to change the phase of two different circular polarizations of electromagnetic-wave propagation in gravitation field and gives polarization rotation for linearly polarized light.[6-8] Polarization observations of radio galaxies put a limit of Δφ ≤ 1 over cosmological distance.[9-14] Further observations to test and measure Δφ to 10 -6 is promising. The natural coupling strength φ is of order 1. However, the isotropy of our observable universe to 10 -5 may leads to a change (ξ)Δφ of φ over cosmological distance scale 10 -5 smaller. Hence, observations to test and measure Δφ to 10 -6 are needed.

8. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 8 Pseudoscalar-Photon Interaction and Axion W.-T. Ni, A Nonmetric Theory of Gravity, preprint, Montana State University, Bozeman, Montana, USA (1973), http://gravity5.phys.nthu.edu.tw. W.-T. Ni, Bull. Am. Phys. Soc., 19, 655 (1974). W.-T. Ni, Phys. Rev. Lett. 38, 301 (1977). S. Weinberg, {\sl Phys. Rev. Lett}. 40, 233 (1978). F. Wilczek, {\sl Phys. Rev. Lett}. 40, 279 (1978). M. Dine {\sl et al.}, {\sl Phys. Lett}. 104B, 1999 (1981). M. Shifman {\sl et al.}, {\sl Nucl. Phys}. B166, 493 (1980). J. Kim, {\sl Phys. Rev. Lett}. 43, 103 (1979). S. L. Cheng, C. Q. Geng and W.-T. Ni, {\sl Phys. Rev.} D52 3132 (1995) and references therein.

9. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 9 Electomagnetic Wave Propagation and Polarization EP W.-T. Ni, "Equivalence Principles and Precision Experiments" pp.~647-651, in Precision Measurement and Fundamental Constants II, ed. by B. N. Taylor and W. D. Phillips, Natl. Bur. Stand. (U.S.), Spec. Publ.~{\bf 617} (1984). W.-T. Ni, "Timing Observations of the Pulsar Propagations in the Galactic Gravitational Field as Precision Tests of the Einstein Equivalence Principle", pp.~441-448 in Proceedings of the Second Asian-Pacific Regional Meeting of the International Astronomical Union, ed. by B. Hidayat and M. W. Feast (Published by Tira Pustaka, Jakarta, Indonesia, 1984). W.-T. Ni, "Equivalence Principles, Their Empirical Foundations, and the Role of Precision Experiments to Test Them", pp.~491-517 in Proceedings of the 1983 International School and Symposium on Precision Measurement and Gravity Experiment, Taipei, Republic of China, January 24-February 2, 1983, ed. by W.-T. Ni (Published by National Tsing Hua University, Hsinchu, Taiwan, Republic of China, June, 1983). M. P. Haugan and T. F. Kauffmann, {\sl Phys. Rev}. D {\bf 52}, 3168 (1995). T. P. Krisher, {\sl Phys. Rev}. D {\bf 44}, R2211 (1991).

10. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 10 Pseudoscalar-Photon Interaction and Astrophysical/Cosmic Polarization Rotation Δ θ (=Δ φ) of Electromagnetic Wave Propagation W.-T. Ni, A Nonmetric Theory of Gravity, preprint, Montana State University, Bozeman, Montana, USA (1973), http://gravity5.phys.nthu.edu.tw. S. M. Carroll, G. B. Field, R. Jackiw, {\sl Phys. Rev}. D {\bf 41}, 1231 (1990). S. M. Carroll and G. B. Field, {\sl Phys. Rev}. D {\bf 43}, 3789 (1991). B. Nodland and J. P. Ralston, {\sl Phys. Rev. Lett}. {\bf 78}, 3043 (1997). J. F. C. Wardle, R. A. Perley, and M. H. Cohen, {\sl Phys. Rev. Lett.} {\bf 79}, 1801 (1997). D. J. Eisenstein and E. F. Bunn, {\sl Phys. Rev. Lett.} {\bf 79}, 1957 (1997). S. M. Carroll and G. B. Field, {\sl Phys. Rev. Lett.} {\bf 79}, 2394 (1997). T. J. Loredo, E. A. Flanagan, and I. M. Wasserman, {\sl Phys, Rev.} {\bf D 56}, 7507 (1997). S. M. Carroll, {\sl Phys. Rev. Lett.} {\bf 81}, 3067 (1998). A. Lue, L. Wang, and M. Kamionkowski, Phys. Rev. Lett. {\bf 83}, 1506 (1999).

11. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 11 Nomenclature in Optics Birefringence: velocity dependent on polarization  linear-polarization to elliptical-polarization Dichroism: absorption varies with polarization Faraday rotation (dependent on wavelength) Cosmic polarization Rotation – not like QED vacuum birefringence (no V [Stokes parameter] produced)

12. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 12 Space contribution to the local polarization rotation angle -- [μΣ13φ,μΔxμ] = | ▽ φ| cos θ Δx0. The time contribution is φ,0 Δx0. The total contribution is (| ▽ φ| cos θ + φ,0) Δx0. (Δx0 > 0) Intergrated: φ(2) - φ(1) 1: a point at the decoupling epoch 2: observation point

13. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 13 Variations and Fluctuations rotationφ(2) - φ(1) rotationφ(2) - φ(1) δφ(2) - δφ(1): δφ(2) variations and fluctuations at the last scattering surface of the δφ(2) - δφ(1): δφ(2) variations and fluctuations at the last scattering surface of the decoupling epoch; δφ(1), at present observation point, fixed decoupling epoch; δφ(1), at present observation point, fixed variance of fluctuation ~ [coupling × 10^(-5)]^2 variance of fluctuation ~ [couplingξ × 10^(-5)]^2 The coupling depends on various cosmological models The coupling depends on various cosmological models

14. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 14 Constraints on cosmic polarization rotation from CMB All consistent with null detection and with one another at 2 σ level

15. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 15 FIVE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP1) OBSERVATIONS: COSMOLOGICAL INTERPRETATION, Komatsu et al., arXiv:0803.0547v2 [astro-ph] 17 Oct 2008 The power spectra of TB and EB correlations constrain a parity-violating interaction, which rotates the polarization angle and converts E to B. The polarization angle could not be rotated more than −5.9 ◦ < α < 2.4 ◦ (95% CL) between the decoupling and the present epoch. I.e. -30 ± 73 mrad (2σ)

16. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 16 References

17. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 17 COSMOLOGICAL MODELS PSEUDO-SCALAR COSMOLOGY, e.g., Brans-Dicke theory with pseudoscalar-photon coupling NEUTRINO NUMBER ASYMMETRY BARYON ASYMMETRY SOME other kind of CURRENT LORENTZ INVARIANCE VIOLATION CPT VIOLATION DARK ENERGY (PSEUDO)SCALAR COUPLING OTHER MODELS

18. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 18

19. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 19 Pseudoscalar Quintessence

20. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 20 JCAP

21. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 21 Neutrino number asymmetry Neutrino number asymmetry is function of electron-neutrino degeneracy parameterξ ν e with ξ ν e = μ ν e (chemical potential) / T νe μ ν e could be ± 0.001

22. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 22 Significance and Outlook Pseudoscalar-photon interaction is proportional to the gradient of the pseudoscalar field. From phenomenological point of view, this gradient could be neutrino number asymmetry, other density current, or a constant vector. In these situations, Lorentz invariance or CPT may effectively be violated. Probing neutrino number asymmetry Better accuracy in CMB polarization observation is expected from PLANCK mission to be launched this year. A dedicated CMB polarization observer in the future would probe this fundamental issue more deeply.

23. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 23 Detectability of Primordial G-Waves

24. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 24 The Gravitational Wave Background from Cosmological Compact Binaries Alison J. Farmer and E. S. Phinney (Mon. Not. RAS [2003]) Optimistic (upper dotted), fiducial (Model A, lower solid line) and pessimistic (lower dotted) extragalactic backgrounds plotted against the LISA (dashed) single- arm Michelson combination sensitivity curve. The ‘ unresolved ’ Galactic close WD – WD spectrum from Nelemans et al. (2001c) is plotted (with signals from binaries resolved by LISA removed), as well as an extrapolated total, in which resolved binaries are restored, as well as an approximation to the Galactic MS – MS signal at low frequencies. Super-ASTROD Region DECIGO BBO Region

25. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 25 LISA LISA consists of a fleet of 3 spacecraft 20 º behind earth in solar orbit keeping a triangular configuration of nearly equal sides (5 × 10 6 km). Mapping the space-time outside super-massive black holes by measuring the capture of compact objects set the LISA requirement sensitivity between 10 - 2 -10 -3 Hz. To measure the properties of massive black hole binaries also requires good sensitivity down at least to 10 -4 Hz. (2017)

26. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 26 ASTROD configuration (baseline ASTROD after 700 days from launch)

27. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 27 Super-ASTROD (1 st TAMA Meeting1996) W.-T. Ni, “ ASTROD and gravitational waves ” in Gravitational Wave Detection, edited by K. Tsubono, M.-K. Fujimoto and K. Kuroda (Universal Academy Press, Tokyo, Japan, 1997), pp. 117-129. With the advance of laser technology and the development of space interferometry, one can envisage a 15 W (or more) compact laser power and 2-3 fold increase in pointing ability. With these developments, one can increase the distance from 2 AU for ASTROD to 10 AU (2×5 AU) and the spacecraft would be in orbits similar to Jupiter's. Four spacecraft would be ideal for a dedicated gravitational-wave mission (Super- ASTROD).

28. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 28 Primordial GW and Super-ASTROD For detection of primordial GWs in space. One may go to frequencies lower or higher than LISA/ASTROD bandwidth where there are potentially less foreground astrophysical sources to mask detection. DECIGO and Big Bang Observer look for gravitational waves in the higher range Super-ASTROD look for gravitational waves in the lower range. Super-ASTROD (ASTROD III) : 3-5 spacecraft with 5 AU orbits together with an Earth-Sun L1/L2 spacecraft and ground optical stations to probe primordial gravitational-waves with frequencies 0.1 μHz - 1 mHz and to map the outer solar system.

29. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 29 Primordial Gravitational Waves [strain sensitivity  (ω^2) energy sensitivity ]

30. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 30 Sensitivity to Primordial GW The minimum detectable intensity of a stochastic GW background is proportional to detector noise spectral power density S_n(f) times frequency to the third power with the same strain sensitivity, lower frequency detectors have an f ^(-3)-advantage over the higher frequency detectors. compared to LISA, ASTROD has 27,000 times (30^3) better sensitivity due to this reason, while Super- ASTROD has an additional 125 (5^3) times better sensitivity.

31. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 31 Primordial Gravitational Waves [strain sensitivity  (ω^2) energy sensitivity ]

32. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 32 Polarization as a tool to test cosmological models and to look into (gravitational) axion and possible dark energy pseudoscalar, CPT, Neutrino Asymmetry, etc. Primordial gravitational waves may possibly be detected by ASTROD/Super- ASTROD and DECIGO/Big Bang Observer

33. W.-T. Ni 2008.11.29. PP-A-QFT SingaporeCosmic polarization rotation, cosmological models & Primordial GW 33 Thank you !