empirical tests of the relativistic gravity: an …summary on lense-thirring measurements lunar...
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Wei-Tou Ni
National Tsing Hua Univ.
EMPIRICAL TESTS
OF THE RELATIVISTIC GRAVITY: An Outlook
2013.06.17. YITP Tests of Relativistic Gravity W.-T. Ni 1
Test of Relativistic Gravity with GW Observations-This week
Emanuele Berti, Compact objects as probes of gravitational physics
Nicolas Yunes, Strong-Field Gravitational Wave Tests of General Relativity
Kent Yagi, Universal I-Love-Q Relations in Neutron Stars and their Applications to Astrophysics, Gravitational Waves and Fundamental Physics
Leo Stein, Isolated and binary neutron star effects in dynamical Chern-Simons and general theories
Hajime Sotani, Neutron stars in scalar-tensor theory and gravitational waves
Atsushi Nishizawa, Test of Alternative Theory of Gravity with Gravitational-wave Polarizations
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ABSTRACT
We first review briefly the historical advances since 1859 when Le Verrier discovered the Mercury perihelion advance anomaly and then report on the present status of the tests of relativistic gravity.
After presenting the empirical foundations of the Einstein Equivalence Principle from laboratory experiments, together with solar-system, astrophysical and cosmological observations, we focus on the current status of dynamical tests in the solar system.
We give an outlook of future relativistic missions and gravitational-wave (GW) missions to test relativistic gravity, and compare their sensitivities. The relevant missions to be addressed are LISA Pathfinder, μSCOPE (MICROSCOPE: MICRO-Satellite à trainée Compensée pour l’Observation du Principle d’Équivalence), GAIA, ASTROD I, ASTROD-GW, NGO/eLISA, and DECIGO.
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Issues in theories of gravity and historical reflections
Dark matter, Modified gravity or Modified dynamics
Dark energy
Inflation theories
Connections among them
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Anomalous orbit perturbation of Uranus and discovery of Neptune in 1820’s
Anomalous orbit perturbation of moon in 19 century and tidal dissipation effect
The discovery of anomalous perihelion advance of Mercury and the genesis of general relativity
MOND: Observational Phenomenology and Relativistic Extensions Famaey & McGaugh lrr 2012
MOND
Modified Newtonian Dynamics
M Milgrom, ApJ 270, 365 (1983)
When a << a0
No dark matter needed
Of minor interests as compared with dark matter in the physics community
a where,)a(aa2NN0
r
GM
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Modified Gravity
Modify Newton’s Law
Rotation curve in galaxies
Cosmology argument
Dark matter vs Modified gravity
General relativity 1915
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References for this talk
W-T Ni, Empirical Foundations of Relativistic Gravity, International Journal of Modern Physics D, 2005;
"100 Years of Gravity and Accelerated Frames---The Deepest Insights of Einstein and Yang-Mills" (Ed. J. P. Hsu and D. Fine, World Scientific, 2005)
W-T Ni, Super-ASTROD: probing primordial gravitational waves and mapping the outer solar system, Class. Quantum Grav. 26 (2009) 075021 (8pp)
W-T Ni, Reports on Progress in Physics (2010)
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Discovery of the Perihelion Advance Anomaly of Mercury
Le Verrier (1811-1877)
an additional 38" per century
anomalous perihelion
advance of Mercury (1859)
1882 Newcomb: 42".95 per century The value more recently was (42".98 0.04)/century. From ephemeris fitting of β: 0.999980.00003 [Pitjeva-Pitjev2013]
Last half of the 19th century: (i) searching for the planet Vulcan, intra-Mercurial matter and the like; (ii) modification of the gravitation law.
Both kinds of efforts were not successful. For modification of the gravitational law, Clairaut's hypothesis, Hall's hypothesis and velocity-dependent force laws were considered. The successful solution awaited for the development of general relativity.
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Einstein Equivalence Principle (1907)
EEP:(Einstein Elevator)
Local physics is that of Special relativity
Study the relationship of Galileo
Equivalence Principle and EEP in a
Relativistic Framework: framework
1970’s
g
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Electromagnetism: Charged particles and photons
)()()16
1( 2/1
II
II
k
kklij
ijkl
I xxdt
dsmgjAFFL
]2
1
2
1[)( 2/1 ijklkjiljlikijkl ggggg ψ
Special Relativity
g framework
Galileo EP constrains to:
)()()16
1( 2/1
II
II
k
kklij
jlikjl
I xxdt
dsmgjAFFL
η
(Pseudo)scalar-Photon Interaction
Various terms in the Lagrangian (W-T Ni, Reports on Progress in Physics, 2010/arXiv) The phenomenological pseudoscalar-photon term (Ni
1973) is later realized in invisible axion and string theory (axiverse, axion stars etc.)
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2013.06.17. YITP
Tests of Relativistic Gravity W.-T. Ni 13
Empirical Constraints: No Birefringence
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Empirical Constraints from Unpolarized EP Experiment: constraint on Dilaton for EM:
ψ = 1 ± 10^(-10)
Cho and Kim, Hierarchy Problem, Dilatonic Fifth, and Origin of Mass, ArXiv0708.2590v1 (4+3)-dim unification with G=SU(2), L<44 μm (Kapner et al., PRL 2007) L<10 μm (Li, Ni, and Pulido Paton, ArXiv0708.2590v1 Lamb shift in Hydrogen and Muonium gr-qc
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Emprirical constraints: H g
(One Metric)
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Constraint on axion: φ < 0.1 Solar-system 1973 (φ < 10^10)
Metric Theories of Gravity
General Relativity
Einstein Equivalence Principle recovered
For a recent exposition, see Hehl &
Obukhov ArXiv:0705.3422v1
Constraints on cosmic polarization rotation from CMB polarization observations [See Ni, RPP 73, 056901 (2010) for detailed references]
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2005 Relativity-parameter determination from inter-planetary radio ranging and from lunar laser ranging
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2013
Lense-Thirring effect on Gyros -- Schiff Effect
L. I. Schiff, Phys. Rev. Lett. 4, 215 (1960).
G. E. Pugh, Research memorandum 11, Weapons System Evaluation Group, the Pentagon, Washington, DC, 1959, reprinted in Nonlinear Gravitodynamics. The Lense-Thirring Effect., edited by R. J. Ruffini and C. Sigismondi (World Scientific, Singapore, 2003), pp. 414–426.
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Summary on Lense-Thirring Measurements
Lunar laser ranging has reported a measurement of the de Sitter solar geodetic effect to 0.7% [14].
Analyses of laser ranging to the LAGEOS and LAGEOS II spacecraft report a 10%–30% measurement of the frame-dragging effect, assuming the GR value for the geodetic precession [15,16].
GP-B provides independent measurements of the geodetic and frame-dragging effects at an accuracy of 0.28% and 19%, respectively.
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LAGEOS orbital gyroscope
The ‘orbital gyroscope’ used to measure the Lense–Thirring effect. The ‘gyroscope’, indicated by the long red arrow, is the combination of the nodal longitudes of the LAGEOS satellites; it is not affected by the huge nodal rate of the LAGEOS satellites because of the Earth’s quadrupole moment.
it is independent of the residual nodal rates due to the error in the Earth quadrupole moment.
The blue drawing shows the orbital configuration of the GRACE satellites used to accurately determine the Earth’s gravity field.
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LAGEOS and Lense-Thirring Effect
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Most recent ephemeris fitting of relativistic effects and dark matter in the solar system from observations of planets and spacecraft
Pitjeva & Pitjev 2013 MNRAS
Results
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(Bounds from estimation)
Dark matter within Saturn’s orbit
Including data related to Odyssey, Mars Reconnais- Sance Orbiter, Mars Express, Venus Express, Cassini, Messenger Observations & CCD observations of the outer planets and satellites at Flagstaff & Table Mountain
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Common Science --- Astrodynamic Equation
n),0,1,(i ) wave-G ( PN2 ) PN1( 3
ij rij
ij
ji ii rr
rr
ij
ijijijijji BAc
Newtonost rrr 2
1 ) P(
12
15.1212122
21311
3
,333333
4
2
5
2
3
2
3
2
2
rrr
rr
rrrr
jij
ij
ij
ij
jikikij
ijjkikjkijjkjkijikij
k
iji
ijij
ij
ij
i
ij
ij
rB
rrrrrrrrrr
rrrrA jij
xxx dotdotii R ) wave-G ( r
+ gal-cosmo term +non-grav term
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Mapping the outer solar system for testing the current models of cosmology
Example: DGP (Dvali, Gabadadze & Porrati) gravity
Single point measurement uncertainties in the ranging data to Mercury and Mars are 200 m and 5-40 m, respectively
Battat, Stubbs and Chandler, PRD 2008, for DGP-like precession:
|dω/dt| < 0.02 ”/century
LLR & Super-ASTROD ranging: single point uncertainties 1 mm 10^(-4) of the DGP effect 20 m. [10 years: 5▪10^(-5) ” ▪ 0.5▪10^(-6) rad/(”) ▪ 5 AU ≈ 20 m], LLR 0.003 AU3%: limited by frame tie & modelling
For Super-ASTROD, 2nd order eccentricity effect can also be measured.
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Aimed accuracy of PPN space parameter γ for various ongoing / proposed experiments (2005)
The types of experiments are given in the parentheses.
MICROSCOPE-Testing WEP to 10^(-15) expected launch: 2015
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LISA Pathfinder 2015
Crucial Test of MOND-TeVeS
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30/24
ASTROD I science goals
6 x10 -6 β
γ
Complete GW Classification http://astrod.wikispaces.com/file/view/GW-classification.pdf (MPLA 25 [2010] pp. 922-935; arXiv:1003.3899v1 [astro-ph.CO])
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Space Detection: LF (100 nHz- 100 mHz) & MF (100 mHz- 10 Hz)
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In addition to adLIGO and adVirgo, KAGRA construction started 2010
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Sensitivity, Angular resolution & Deployment
Angular resolution ~ S/N ratio
Solar orbit Deployment after separation of launcher:
1-2 years with propellent mass ratio 0.25 to 0.55
Using near Hohmann orbit and Venus flyby
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From Yagi 2013 (left & above)
Scientific goals
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in both GR and Brans-Dicke theory
For GR, L is equal to 2 or more, the dominant term is
For Brans-Dicke theory, we need to consider monopole and dipole parts. But, because of the conservation of mass and linear momentum in Newtonian theory, the monopole moment and dipole moment are constant at lowest order in the expansion, and their time derivatives vanish. As a result, the energy loss due to monopole scalar waves is of the same order as that due to quadrupole radiation in general relativity while the energy loss due to dipole scalar waves is of O(2) order smaller. Detailed consideration of non-linear effects does not change the leading order.
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Spherically symmetric core collapse supernovae at the distance 10kpc (Monopole radiation) with KAGRA.
The progenitor mass 20M⊙/5M⊙and
ωBD = 500, 1000, 2000, 4000, 8000, 16000, 40000, 80000, 160000.
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KAGRA
20M⊙
5M⊙
20M⊙ 5M⊙
ωBD
1208.4596 K. Hayama and A. Nishizawa
Shibata et al. 1994
For binaries (2 scales in weakness of the field) in scalar-tensor theories: discussion with Kent
Monopole radiation ~ quadrupole
radiation
Dipole radiation ~ (s1 − s2)^2/O(orbital
potential) x monopole radiation
For quasi-circular orbit: (s1 − s2) ~ 0.1 for
neutron star and white dwarf binary;
O(orbital potential) could be 1 ppm, so
dipolar radiation could be stronger
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Cassini measurements ωBD > 40 000 for scalar masses ms < 2.5 x 10^(-20) eV [or Compton wavelengths λs > 5 x 10^10 km], to 95%
confidence.
Observations of the Nordtvedt effect using lunar laser ranging experiments yield ωBD > 1000 for ms < 2.5 x 10^(-20) eV.
Observations of the orbital period derivative of the quasicircular white dwarf-neutron star binary PSR J1012 þ 5307 yield ωBD > 1250 for ms < 10 ^(-20) eV (λs > 1.2�x 10^(11) km).
radiation damping in the eccentric white dwarf-neutron star binary PSR J1141 � 6545 requires the extension of this work to eccentric orbits.
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Tests of relativistic implementation of MOND theories: MNRAS, Freire et al.2012
For generic TeVeS-like models with | β0 | > 0.1, we find again that PSR J1738+0333 is the most constraining binary pulsar. TeVeS (β0 = 0) is saved.
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From Yagi’s review 2013 and Berti’s talk
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Thank You!
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IJMPD
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