1. Geophysical tests of gravitational physics with superconducting gravimeters
Sachie Shiomi
Space Geodesy Laboratory,
Department of Civil Engineering,
National Chiao Tung University,
Hsinchu, Taiwan

2. Contents Introduction
Superconducting Gravimeters (SGs)
Examples of applications to gravitational physics
The global network of SGs
Application 1: Testing the universality of free-fall
Application 2: Searching for dilatonic waves
Summary

3. Superconducting gravimeter (SG)
Sensitive and stable at low frequencies
1 m
Hsinchu SG, operated by NCTU and CMS

4. Gravimeter Sensing Unit
Working principle
Sphere is levitated by magnetic fields induced by currents in the superconducting levitation coils.
Motion of the sphere is monitored by capacitor plates.
Φ~ 2.5 cm
~4.2 K
J. M. Goodkind, Review of Scientific Instruments 70 (1999)

5. Applications to gravitational physics
Earliest work (1976)
Search for evidence of a preference frame
(Warburton and Goodkind, Astrophysical Journal, 1976.)
More recent works, e.g.
Test of the inverse-square law
(Goodkind et al PRD 1993, Baldi et al PRD, 2001)
Measurement of gravitational constant G
(Baldi et al PRD, 2005)

6. The GGP network
The Global Geodynamics Project (GGP) network of superconducting gravimeters (1997~): about 25 operating sites.
To study geophysical signals in global nature, i.e. oscillation of the inner core, polar motion and wobbles.
D. Crossley, Journal of Geodynamics 38 (2004)

7. Currently operating
Stopped
To be installed
Newly installed
D. Crossley

8. Applications of the global network to gravitational physics
We investigate possible applications of the GGP network to study gravitational physics.
One of such applications is testing the universality of free-fall.

9. Testing the universality of free-fall

10. Universality of free-fall
Every material (point mass) in a given external gravitational field falls at the same rate.

11. Motivations of testing the universality
Fundamental principle
It should be tested as precisely as possible.
New physics?
Theories towards the unification of the four fundamental forces predict new interactions that violate the principle.

12. Proposed new forces (spin-independent)
Motivated by
Bosons (Spin)
Mass
Charge
References (year)
Conservation of baryon charge
Vector bosons (1)
massless B
Lee and Yang (1955)
Supersymmetry
U-bosons (1)
Massive
(very light)
B, Iz
Fayet(1986)
String theory
Dilatons(0)
Moduli(0)
massive
(millimeter range)
Ordinary matter
B, Iz, E
Fujii(1971);Taylor and Veneziano (1988)
Damour and Polyakov(1994)
Dimopoulos and Giudice(1996)
Composition dependent

13. Modification of Newton’s law
V(r)
Yukawa-potential type

14. Current limits
Fischbach and Talmadge, The Search for Non-Newtonian Gravity (Springer-Verlag, 1999)

15. The necessity of variety in experimental approaches
The universality has to be tested for various putative charges, using different kinds of test bodies, at different ranges.
To confirm experimental results, it should be tested by at least two different experimental methods.

16. The concept
Sun
If the universality were violated, the inner core would move relative to the rest part of the Earth.
Surface gravity changes

17. Test bodies: inner core and the rest
Chemical composition
Density [kg m-3]
Inner core (iron, nickel): ~ 13000
The rest (silicon oxides): ~ 5400
Gravitational binding energy
Inner core: -3.7 ×10-11
The rest: ×10-10

18. Best observation points
Taiwan
Summer
Sun
Earth SG
In Spring and Autumnal equinox points: on the equator
In Summer and Winter solstices: on Tropic of Cancer or Capricorn

19. Equation of motion of the inner core
Gravitational stiffness
Damping effect
Violation effect
S. Shiomi, Physical Review D 74, (2006)

20. When the damping coefficient (k) is sufficiently small:
Forced oscillation
When the damping coefficient (k) is sufficiently small:
Surface gravity changes
10-12 ms-2

21. Expected sensitivity Current limits: a few parts in 1013
;nearly four orders of magnitude improvement is necessary.

22. Improving the sensitivity (1)
Carrying out coincidence measurements at two observatories located opposite side of the Earth near the equators.

23. Improving the sensitivity (2)
Development of the data analysis method to extract weak signals.
e.g.
Non-Linear Damped Harmonic Analysis method (S. Rosat et al, J. Geodyn. in press)

24. Summary: expected signals
Direction
along the Earth-Sun line
Frequency
once per day
once per year

25. Future works Improving noise reduction methods
Identification of environmental noise
Data analyses to extract weak signals
Figuring out the optimum scheme of global observations
e.g. coincidence measurements
Improvements of the sensitivity of SGs
Application of elaborate Earth models

26. Conclusions
The universality of free-fall can be tested using a superconducting gravimeter installed near the equator to ~10-9.
Some improvements can be expected from global observations and applications of advanced data analysis methods.

27. Search for composition-dependent dilatonic waves

28. Introduction
String theory predicts the existence of relic background of the dilaton (a scalar partner of the graviton).
Ordinary macroscopic test masses have dilatonic charges, which depend on their internal compositions.
The response of the test masses to dilatonic waves is non geodesic.
M. Gasperini, Phys. Lett. B 470, 67 (1999)

29. The concept

30. Estimation of upper limits (1)
Spectrum of the displacement ( l ) at resonance
Dimensionless energy density for massless dilaton

31. Estimation of upper limits (2)
From residual gravity data,
an upper limit on the displacement is
1.1 ×10-4 m Hz-1/2 at 7 ×10-5 Hz.
(S. Rosat et al, J. of Geodyn. 38 (2004))
Effective viscosity: 10-3 ~ Pa s
(R.A. Secco, A Handbook of Physical Constants)
S. Shiomi, “Geophysical search for dilatonic waves” (submitted in 2007)

32. Nucleosynthesis and measurements of cosmic microwave background:
To reach this limit, the effective viscosity has to be smaller than ~ 2 × 106 Pa s.

33. Conclusions
Dilatonic waves can be searched for using superconducting gravimeters.
The sensitivity is currently limited by the uncertainty in the Earth model.
If the effective viscosity were determined to be smaller than ~ 2 × 106 Pa s, this method would provide an upper limit better than the astrophysical limits.

34. Other possible future applications
Improved tests of the existence of a preference frame and an anisotropy of the gravitational constant.
Direct detection of gravitational waves using the Earth as the receiver.
Measurement of G
Tests for a distant dependence, time dependence and a spatial anisotropy.
Improved tests of the inverse square law.
J. M. Goodkind, Review of Scientific Instruments 70 (1999)

35. Summary
Superconducting gravimeters have been proved to be stable and sensitive in geophysical studies and also they have been used to study gravitational physics since 1970’s.
The global network of superconducting gravimeters has been developed to study the Earth’s interior. By using the Earth as the test body, we investigate possible applications of the network to gravitational physics.
We have discussed the geophysical test of the universality of free-fall and the search for dilatonic waves.

36. Any new ideas for possible applications of SGs are welcome.
Thank you.
Any new ideas for possible applications of SGs are welcome.