Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale

Abstract

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...

The cosmological constant puzzle

“…At short distances, recent torsion balance experiments [15] have found that Newton's Inverse Square Law (ISL) holds down to a length scale of 56 µm. This result is especially interesting because this length is less than the dark-energy length scale λ = (hc/ρ vac ) 1 4 ∼ 85µm corresponding to energy density ρ vac ∼ 3.8 keV/cm 3 (or (0.002 eV) 4 ) extracted from dark energy astrophysics experiments.…”

Estimate for the size of the compactification radius of a one extra dimension universe

“…That is a very interesting relation from the perspective of the hierarchy problem, because it allows for the effective mass M 4 that we observe to be huge even when the true mass M 4+n is not that big. Just to put some numbers, let us consider r c 1 µm ⇒ (r c ) −1 0.18 eV , which is just below the lower bound for the experimental validity of newtonian gravitation [10]. This automatically gives the following values for M 4+n…”

Lagrange multiplier and Wess-Zumino variable as extra dimensions in the torus universe

“…Also, since we obtained the deviation from Newton's 2nd law for free particle constrained to the surface of a 3-torus, relation (3.48), any test of the gravitational inverse-square law can be used to investigate our model [86,87]. For instance, to observe the transition from inverse-square law of Newtonian gravitation imposed via extra dimensions in brane world models, some measurements such as submillimeter measurement of gravity are proposed and can be used to test our model [71,[88][89][90][91].…”