extra dimensions, dark energy and the gravitational inverse-square law ? liam j. furniss, humboldt...
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Extra Dimensions, Dark Energy and the GravitationalInverse-Square Law
?
Liam J. Furniss, Humboldt State University
Motivation
• Some string theories predict stronger gravity at short distances.
• Accelerating expansion of the Universe could be explained by weaker gravity at short distances.
• Testing gravitation in this regime offers us a chance to test both theories at once.
ModelingTo model any “new” behavior we use the Yukawa potential:
1 2 / 1Gmm rV r er
• Stepped pendulum with large, modulated attractor plate
• Newtonian torque is weak and analytic
• Principal challenge is achieving ~0.1mm separation
Our Method
R
Modulateseparation
Our Method
Observed Yukawa component of torque:2 /s
Y p aN G RA e
Out[12]=
2 4 6 8 1 0 1 2
0 .0 5
0 .1 0
0 .1 5
0 .2 0
Yukawa
N ewtonian
0 T 2T
Time
Tor
que
(fN
·m)
Out[12]=
2 4 6 8 1 0 1 2
0 .0 5
0 .1 0
0 .1 5
0 .2 0
Yukawa
N ewtonian
0 T 2T
Time
Tor
que
(fN
·m)
Out[12]=
2 4 6 8 1 0 1 2
0 .0 5
0 .1 0
0 .1 5
0 .2 0
Yukawa
N ewtonian
0 T 2T
Time
Tor
que
(fN
·m)
Sensitivity
• Torque sensitivity fundamentally limited by:– Thermal noise in the torsion fiber– Optical readout uncertainty due to torsion
pendulum resonance
• Thermal noise caused by random atomic motion varies with signal frequency:
4
QB
thk T
N
Sensitivity• Equation of motion for torsion pendulum:
• Optical readout uncertainty also varies with signal frequency:
2 22
20
11
Qro roN
1Q
iN I b
Sensitivity
Frequency (Hz)
Out[67]=
0 .0 0 1 0 0 .0 1 0 00 .0 0 5 00 .0 0 2 0 0 .0 0 3 00 .0 0 1 5 0 .0 0 7 0
1 .0 1 0 15
5 .0 1 0 16
2 .0 1 0 15
3 .0 1 0 16
1 .5 1 0 15
7 .0 1 0 16
Tota l N ois e
The rmal N ois e
R e adout N ois e
Tor
que
nois
e (N
·m/
Hz)
Frequency (Hz)
Out[67]=
0 .0 0 1 0 0 .0 1 0 00 .0 0 5 00 .0 0 2 0 0 .0 0 3 00 .0 0 1 5 0 .0 0 7 0
1 .0 1 0 15
5 .0 1 0 16
2 .0 1 0 15
3 .0 1 0 16
1 .5 1 0 15
7 .0 1 0 16
Tota l N ois e
The rmal N ois e
R e adout N ois e
Tor
que
nois
e (N
·m/
Hz)
2 2ro thN N N
Limiting Systematic Error
• Other sources of systematic noise include:– Viscous damping of pendulum motion– Electrostatic charge buildup– Seismic vibrations
• Numerous experimental steps to eliminate these factors:– High vacuum (μTorr) – Electrostatic shield– High resolution tilt sensor– Magnetic damper
Thermal Isolation
Tests of our isolation chamber and temperature controller show greatly increased thermal stability.
1 0 4 0 .0 0 1 0 .0 1 0 .11 0 4
0 .0 0 1
0 .0 1
0 .1
1
1 0
Frequency (Hz)
Tem
pera
ture
noi
se (
deg
C/
Hz)
1 0 4 0 .0 0 1 0 .0 1 0 .11 0 4
0 .0 0 1
0 .0 1
0 .1
1
1 0
Frequency (Hz)
Tem
pera
ture
noi
se (
deg
C/
Hz)
Apparatus
Thermal Isolation Enclosure
Vacuum Chamber
Optical Readout
Laser Beam
Pendulum
Torsion Fiber
Attractor
• Construction of thermal enclosure, vacuum chamber, magnetic damper, optical system and readout electronics complete
• Preliminary pendulum tests this summer
• Week-long run of experiment by year end
Provided we can restrict noise to near its fundamental limit, we expect to exceed previous experiments by a factor of 100
Expectations
Our Research• Tests theories of the very large and the very
small simultaneously• Stepped pendulum is both simple and sensitive• 100x more sensitivity than previous experiments• Official experimental runs by year end Financial support provided by Research Corporation grant CC6839 and the HSU
College of Natural Resources and Sciences
References1. N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali, “New dimensions at a millimeter to a fermi and superstrings at a TeV,” Phys. Lett. B 436, 257 (1998).2. D.B. Kaplan and M.B. Wise, “Couplings of a light dilaton and violations of. the equivalence principle,”JHEP 0008, 037 (2000).3. S. Perlmutter et al., "Measurements of W and from 42 high-redshift supernovae,” Astrophys. J. 517, 565 (1999).4. C.D. Hoyle et al., “Submillimeter tests of the gravitational inverse-square law,” Phys. Rev. D 70 042004 (2004).5. R. Sundrum, “Fat gravitons, the cosmological constant and submillimeter tests,” Phys. Rev. D 69, 044014 (2004).6. D.J. Kapner et al., “Tests of the gravitational inverse-square law below the dark-energy length scale,” Phys. Rev. Lett. 98 021101 (2007). 7. E.G. Adelberger, N.A. Collins, and C.D. Hoyle, “Analytic expressions for gravitational inner multipole moments of elementary solids and for the force between two rectangular solids,” Class. Quant. Grav. 23 125-136 (2006).