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).