COSMIC POLARIZATION ROTATION COSMOLOGICAL MODELS AND Detectability

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 1

CMB Polarization Observation l In 2002, DASI microwave interferometer observed the polarization of the cosmic background. l With the pseudoscalar-photon interaction , the polarization anisotropy is shifted relative to the temperature anisotropy. l 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. 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 2

CMB Polarization Observation l In 2005, the DASI results were extended (Leitch et al. ) and observed by CBI (Readhead et al. ) and CAPMAP (Barkats et al. ) l In 2006, BOOMERANG CMB Polarization l DASI, CBI, and BOOMERANG detections of Temperature-polarization cross correllation l 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. 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 3

WMAP 3 year Polarization Maps TT TT TE foreground EE BB(r=0. 3) 2008. 11. 29. PP-A-QFT Singapore BB(lensing) Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 4

Pseudo-scalars: Pseudoscalar-Photon Coupling 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 5

≈ ξ φ, μ A ν F ~ μ ν ≈ ξ (1/2)φ FμνF~μν (Mod Divergence) 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 6

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] l Polarization observations of radio galaxies put a limit of Δφ ≤ 1 over cosmological distance. [9 -14] l Further observations to test and measure Δφ to 10 -6 is promising. l 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. l 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 7

Pseudoscalar-Photon Interaction and Axion l l l l l W. -T. Ni, A Nonmetric Theory of Gravity, preprint, Montana State University, Bozeman, Montana, USA (1973), http: //gravity 5. 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}. 104 B, 1999 (1981). M. Shifman {sl et al. }, {sl Nucl. Phys}. B 166, 493 (1980). J. Kim, {sl Phys. Rev. Lett}. 43, 103 (1979). S. L. Cheng, C. Q. Geng and W. -T. Ni, {sl Phys. Rev. } D 52 3132 (1995) and references therein. 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 8

Electomagnetic Wave Propagation and Polarization EP l l l 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}, R 2211 (1991). 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 9

Pseudoscalar-Photon Interaction and Astrophysical/Cosmic Polarization Rotation Δθ (=Δφ) of Electromagnetic Wave Propagation l l l l l W. -T. Ni, A Nonmetric Theory of Gravity, preprint, Montana State University, Bozeman, Montana, USA (1973), http: //gravity 5. 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 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). 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 10

Nomenclature in Optics l Birefringence: velocity dependent on polarization linear-polarization to elliptical-polarization l Dichroism: absorption varies with polarization l Faraday rotation (dependent on wavelength) l Cosmic polarization Rotation – not like QED vacuum birefringence (no V [Stokes parameter] produced) 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 11

Space contribution to the local polarization rotation angle -- [μΣ 13φ, μΔxμ] = |▽φ| cos θ Δx 0. The time contribution is φ, 0 Δx 0. The total contribution is (|▽φ| cos θ + φ, 0) Δx 0. (Δx 0 > 0) Intergrated: φ(2) - φ(1) 1: a point at the decoupling epoch 2: observation point 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 12

Variations and Fluctuations rotationφ(2) - φ(1) l 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 l <[δφ(2) - δφ(1)]^2> variance of fluctuation ~ [couplingξ × 10^(-5)]^2 [coupling l The coupling depends on various cosmological models l 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 13

Constraints on cosmic polarization rotation from CMB All consistent with null detection and with one another at 2 σ level 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 14

FIVE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP 1) OBSERVATIONS: COSMOLOGICAL INTERPRETATION, Komatsu et al. , ar. Xiv: 0803. 0547 v 2 [astro-ph] 17 Oct 2008 l 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) 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 15

References 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 16

COSMOLOGICAL MODELS l l l l 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 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 17

2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 18

Pseudoscalar Quintessence 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 19

JCAP 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 20

Neutrino number asymmetry is function of electron-neutrino degeneracy parameterξν e with ξν e = μν e (chemical potential) / Tνe l μν ecould be ± 0. 001 l 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 21

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. l Probing neutrino number asymmetry l 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. l 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 22

Detectability of Primordial G-Waves 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 23

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) singlearm Michelson combination sensitivity curve. The‘unresolved’ Galactic close WD–WD spectrum from Nelemans et al. (2001 c) 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. 2008. 11. 29. PP-A-QFT Singapore Super-ASTROD Region DECIGO BBO Region Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 24

LISA consists of a fleet of 3 spacecraft 20º 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) 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 25

ASTROD configuration (baseline ASTROD after 700 days from launch) 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 26

Super-ASTROD (1 st TAMA Meeting 1996) 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. l 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). l 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 27

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. l DECIGO and Big Bang Observer look for gravitational waves in the higher range l Super-ASTROD look for gravitational waves in the lower range. l Super-ASTROD (ASTROD III) : 3 -5 spacecraft with 5 AU orbits together with an Earth-Sun L 1/L 2 spacecraft and ground optical stations to probe primordial gravitational-waves with frequencies 0. 1 μHz - 1 m. Hz and to map the outer solar system. l 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 28

Primordial Gravitational Waves [strain sensitivity (ω^2) energy sensitivity] 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 29

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 l with the same strain sensitivity, lower frequency detectors have an f ^(-3)-advantage over the higher frequency detectors. l 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. l 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 30

Primordial Gravitational Waves [strain sensitivity (ω^2) energy sensitivity] 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 31

l Polarization as a tool to test cosmological models and to look into (gravitational) axion and possible dark energy pseudoscalar, CPT, Neutrino Asymmetry, etc. l Primordial gravitational waves may possibly be detected by ASTROD/Super-ASTROD and DECIGO/Big Bang Observer 2008. 11. 29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 32

l. Thank 2008. 11. 29. PP-A-QFT Singapore you ! Cosmic polarization rotation, cosmological models & Primordial GW W. -T. Ni 33