1. Extra Dimensions, Dark Energy and the Gravitational Inverse-Square Law ? Liam J. Furniss, Humboldt State University

2. 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.

3. Modeling To model any “new” behavior we use the Yukawa potential:

4. Stepped pendulum with large, modulated attractor plate Newtonian torque is weak and analytic Principal challenge is achieving ~0.1mm separation Our Method R Modulate separation

5. Our Method Observed Yukawa component of torque:

6. 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:

7. Sensitivity Equation of motion for torsion pendulum: Optical readout uncertainty also varies with signal frequency:

8. Sensitivity

9. 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

10. Thermal Isolation Tests of our isolation chamber and temperature controller show greatly increased thermal stability.

11. 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

12. Provided we can restrict noise to near its fundamental limit, we expect to exceed previous experiments by a factor of 100 Expectations

13. 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 References 1. 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).