We conducted three torsion-balance experiments to test the gravitational inverse-square law at separations between 9.53 mm and 55 µm, probing distances less than the dark-energy length scale λ d = 4 hc/ρ d ≈ 85 µm. We find with 95% confidence that the inverse-square law holds (|α| ≤ 1) down to a length scale λ = 56 µm and that an extra dimension must have a size R ≤ 44 µm.PACS numbers: 95.36.+x,04.80.Cc,12.38.Qk Recent cosmological observations [1,2,3] have shown that 70% of all the mass and energy of the Universe is a mysterious "dark energy" with a density ρ d ≈ 3.8 keV/cm 3 and a repulsive gravitational effect. This darkenergy density corresponds to a distance λ d = 4 hc/ρ d ≈ 85 µm that may represent a fundamental length scale of gravity [4,5]. Although quantum-mechanical vacuum energy should have a repulsive gravitational effect, the observed ρ d is between 10 60 to 10 120 times smaller than the vacuum energy density computed according to the standard laws of quantum mechanics. Sundrum [6] has suggested that this huge discrepancy (the "cosmological constant problem") could be resolved if the graviton were a "fat" object with a size comparable to λ d that would prevent it from "seeing" the short-distance physics that dominates the vacuum energy. His scenario implies that the gravitational force would weaken for objects separated by distances s < ∼ λ d . Dvali, Gabadaze and Senjanovíc [7] argue that a similar weakening of gravity could occur if there are extra time dimensions. In their scenario, the standard model particles are localized in "our" time, while the gravitons propagate in the extra time dimension(s) as well. Other scenarios predict the opposite behavior: the extra space dimensions of Mtheory would cause the gravitational force to get stronger for s < ∼ R where R is the size of the largest compactified dimension [8]. These considerations, plus others involving new forces from the exchange of proposed scalar or vector particles[9] motivated the tests of the gravitational inverse-square law we report in this Letter.Our tests were made with a substantially upgraded version of the "missing mass" torsion-balance instrument used in our previous inverse-square-law tests [10,11]. The instrument used in this work [12], shown in Fig. 1, consisted of a torsion-pendulum detector suspended by a thin ≈ 80-cm-long tungsten fiber above an attractor that was rotated with a uniform angular velocity ω by a geared-down stepper motor. The detector's 42 test bodies were 4.767-mm-diameter cylindrical holes machined into a 0.997-mm-thick molybdenum detector ring. The hole centers were arrayed in two circles, each of which had 21-fold azimuthal symmetry. The attractor had a similar 21-fold azimuthal symmetry and consisted of a 0.997 mm thick molybdenum disc with 42 3.178-mm-diameter holes mounted atop a thicker tantalum disc containing 21 6.352-mm-diameter holes. The gravitational interaction between the missing masses of the detector and attractor holes applied a torque on the detector that oscillated 21 times for eac...

Motivated by higher-dimensional theories that predict new effects, we tested the gravitational 1/r(2) law at separations ranging down to 218 microm using a 10-fold symmetric torsion pendulum and a rotating 10-fold symmetric attractor. We improved previous short-range constraints by up to a factor of 1000 and find no deviations from Newtonian physics.

Motivated by a variety of theories that predict new effects, we tested the gravitational 1/r 2 law at separations between 10.77 mm and 137 µm using two different 10-fold azimuthally symmetric torsion pendulums and rotating 10-fold symmetric attractors. Our work improves upon other experiments by up to a factor of about 100. We found no deviation from Newtonian physics at the 95% confidence level and interpret these results as constraints on extensions of the Standard Model that predict Yukawa or power-law forces. We set a constraint on the largest single extra dimension (assuming toroidal compactification and that one extra dimension is significantly larger than all the others) of R * ≤ 160 µm, and on two equal-sized large extra dimensions of R * ≤ 130 µm. Yukawa interactions with |α| ≥ 1 are ruled out at 95% confidence for λ ≥ 197 µm. Extra-dimensions scenarios stabilized by radions are restricted to unification masses M * ≥ 3.0 TeV/c 2 , regardless of the number of large extra dimensions. We also provide new constraints on power-law potentials V (r) ∝ r −k with k between 2 and 5 and on the γ5 couplings of pseudoscalars with m ≤ 10 meV/c 2 .

We use data from our recent search for violations of the gravitational inverse-square law to constrain dilaton, radion, and chameleon exchange forces as well as arbitrary vector or scalar Yukawa interactions. We test the interpretation of the PVLAS Collaboration effect and a conjectured "fat-graviton" scenario and constrain the gamma_{5} couplings of pseuodscalar bosons and arbitrary power-law interactions.

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