empirical tests of the relativistic gravity: an …summary on lense-thirring measurements lunar...

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


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.


Issues in theories of gravity and historical reflections

Dark matter, Modified gravity or Modified dynamics

Dark energy

Inflation theories

Connections among them


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


Modified Gravity

Modify Newton’s Law

Rotation curve in galaxies

Cosmology argument

Dark matter vs Modified gravity

General relativity 1915



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)


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.


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


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.)


2013.06.17. YITP

Tests of Relativistic Gravity W.-T. Ni 13

Empirical Constraints: No Birefringence


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


Emprirical constraints: H g

(One Metric)


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]



2005 Relativity-parameter determination from inter-planetary radio ranging and from lunar laser ranging


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.


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.


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.


LAGEOS and Lense-Thirring Effect


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


(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


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


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.


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


LISA Pathfinder 2015

Crucial Test of MOND-TeVeS


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])


Space Detection: LF (100 nHz- 100 mHz) & MF (100 mHz- 10 Hz)

http://astrod.wikispaces.com/file/view/GW-classification.pdf



http://xxx.lanl.gov/abs/1003.3899v1

In addition to adLIGO and adVirgo, KAGRA construction started 2010


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


From Yagi 2013 (left & above)

Scientific goals


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.


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.


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


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.


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.


From Yagi’s review 2013 and Berti’s talk



Thank You！


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empirical tests of the relativistic gravity: an …summary on lense-thirring measurements lunar...

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