cosmic polarization rotation & cosmological models and detectability of primordial g-waves

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COSMIC POLARIZATION ROTATION & COSMOLOGICAL MODELS

AND Detectability of Primordial G-Waves

Wei-Tou NiWei-Tou NiCenter for Gravitation and Cosmology, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing,

CHINANational Astronomical Observatories, Chinese Academ

y of Sciences, Beijing, CHINA

2008.11.29. PP-A-QFT Singapore Cosmic polarization rotation, cosmological models & Primordial GWCosmic polarization rotation, cosmological models & Primordial GW 2W.-T. Ni

CMB Polarization ObservationCMB Polarization ObservationIn 2002, DASI microwave interferometer observ

ed the polarization of the cosmic background. With the pseudoscalar-photon interaction , the p

olarization 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.


CMB Polarization ObservationCMB Polarization ObservationIn 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 PolarizationDASI, CBI, and BOOMERANG detections of

Temperature-polarization cross correllationPlanck 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.


WMAP 3 year Polarization MapsWMAP 3 year Polarization Maps

TTTT

TE

EE

BB(r=0.3)BB(lensing)

foreground


Pseudo-scalars:Pseudo-scalars: Pseudoscalar-Photon Coupling Pseudoscalar-Photon Coupling


≈ ≈ ξξφφ,,μμ AAννFF~~μμνν ≈ ≈ ξξ (1/2)(1/2)φφ FFμμννFF~~μμνν

(Mod Divergence)(Mod Divergence)


Change of Polarization due to Change of Polarization due to Cosmic PropagationCosmic 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.


Pseudoscalar-Photon Pseudoscalar-Photon Interaction andInteraction and AxionAxion

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 (198

0). 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.


Electomagnetic Wave Propagation and Polarization Electomagnetic Wave Propagation and Polarization EPEP

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).


Pseudoscalar-Photon Interaction and Astrophysical/Cosmic Pseudoscalar-Photon Interaction and Astrophysical/Cosmic Polarization Rotation Polarization Rotation ΔΔθθ (= (=ΔΔφφ)) of Electromagnetic Wave of Electromagnetic Wave

PropagationPropagation

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}, 1

801 (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).


Nomenclature in OpticsNomenclature 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)


Space contribution to the local polarization rotation Space contribution to the local polarization rotation angle -- [μΣ13angle -- [μΣ13φ,φ,μμΔΔxμ] = |▽xμ] = |▽φφ| cos | cos θθ ΔΔx0. The time x0. The time contribution is contribution is φ,0φ,0 ΔΔx0. The total contribution is (|x0. The total contribution is (|

▽▽φφ| cos | cos θθ + + φ,0φ,0) ) ΔΔx0. x0. ( (ΔΔx0x0 > 0) > 0)

Intergrated:φ(2) - φ(1)φ(2) - φ(1)1: a point at the 1: a point at the decoupling epochdecoupling epoch2: observation 2: observation pointpoint


Variations and FluctuationsVariations and Fluctuations

rotationφ(2) - φ(1)rotationφ(2) - φ(1) δδφ(2) - φ(2) - δδφ(1): φ(1): δδφ(2) variations and fluctuations at φ(2) variations and fluctuations at

the last scattering surface of thethe last scattering surface of the decoupling epoch; decoupling epoch; δδφ(1), at present observation φ(1), at present observation

point, fixedpoint, fixed <[<[δδφ(2) - φ(2) - δδφ(1)]^2> variance of fluctuation φ(1)]^2> variance of fluctuation ~ ~

[coupling[couplingξ × 10^(-5)]^2 × 10^(-5)]^2 The coupling depends on various cosmological The coupling depends on various cosmological

modelsmodels


Constraints on cosmic polarization Constraints on cosmic polarization rotation from CMBrotation from CMB

All consistent with null detection and with one another at 2 σ level


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)


ReferencesReferences


COSMOLOGICAL MODELSCOSMOLOGICAL MODELS PSEUDO-SCALAR COSMOLOGY, e.g., Bran

s-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 COUP

LING OTHER MODELS


Pseudoscalar QuintessencePseudoscalar Quintessence


JCAPJCAP


Neutrino number asymmetryNeutrino number asymmetry Neutrino number asymmetry is function of

electron-neutrino degeneracy parameterξν e with ξν

e = μν e (chemical potential) / Tνe

μν ecould be ± 0.001


Significance and OutlookSignificance 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 expe

cted from PLANCK mission to be launched this year. A dedicated CMB polarization observer in the future would probe this fundamental issue more deeply.


Detectability of

Primordial G-Waves


The Gravitational Wave Background from The Gravitational Wave Background from Cosmological Compact BinariesCosmological Compact Binaries

Alison J. Farmer and E. S. Phinney (Mon. Not. RAS [2003])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 GalacticMS–MS signal at low frequencies.

Super-ASTRODRegion DECIGO

BBO Region


LISALISA LISA consists of a fleet of 3 spacecraft 20º behind earth in solar orbit keeping a triangular configuration of nearly equal sides (5 × 106 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)


ASTROD configuration (baseline ASTROD configuration (baseline ASTROD after 700 days from launch)ASTROD after 700 days from launch)

Sun

Inner OrbitEarth Orbit

Outer Orbit

Launch Position

.

Earth L1 point S/C (700 days after launch)

S/C 2

S/C 1

.

.

1

1*

3*3

2*

22n̂

1n̂

3n̂U1

L2

-V3 L1

U3

-V2

U2

-V1L3

.


Super-ASTROD (1Super-ASTROD (1stst TAMA Meeting1996) TAMA Meeting1996)W.-T. Ni, “ASTROD and gravitational waves” in W.-T. Ni, “ASTROD and gravitational waves” in Gravitational WGravitational W

ave Detectionave Detection, , edited by K. Tsubono, M.-K. Fujimoto and K. Kuroda edited by K. Tsubono, M.-K. Fujimoto and K. Kuroda

(Universal Academy Press, Tokyo, Japan, 1997), pp. 117-129.(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).


Primordial GW and Super-ASTRODPrimordial 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.


Primordial Gravitational WavesPrimordial Gravitational Waves[[strain sensitivity strain sensitivity ( (ωω^2) energy sensitivity^2) energy sensitivity]]


Sensitivity to Primordial GWSensitivity 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.


Primordial Gravitational WavesPrimordial Gravitational Waves[[strain sensitivity strain sensitivity ( (ωω^2) energy sensitivity^2) energy sensitivity]]


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


Thank you !

cosmic polarization rotation & cosmological models and detectability of primordial g-waves

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