Submillimeter spatial oscillations of Newton’s constant: Theoretical models and laboratory tests

Abstract

We investigate the viability of sub-millimeter wavelength oscillating deviations from the Newtonian potential at both the theoretical and the experimental/observational level. At the theoretical level such deviations are generic predictions in a wide range of extensions of General Relativity (GR) including f (R) theories, massive Brans-Dicke (BD)-scalar tensor theories, compactified extra dimension models and nonlocal extensions of GR. However, the range of parameters associated with such oscillating deviations is usually connected with instabilities present at the perturbative level. An important exception emerges in nonlocal gravity theories where oscillating deviations from Newtonian potential occur naturally on sub-millimeter scales without any instabilities. As an example of a model with unstable Newtonian oscillations we review an f (R) expansion around General Relativity of the form f (R) = R + 1 6m 2 R 2 with m 2 < 0 pointing out possible stabilization mechanisms. As an example of a model with stable Newtonian oscillations we discuss nonlocal gravity theories. If such oscillations are realized in Nature on sub-millimeter scales, a signature is expected in torsion balance experiments testing the validity of Newton's law. We search for such a signature in the torsion balance data of the Washington experiment [1] (combined torque residuals of experiments I, II, III) testing Newton's law at sub-millimeter scales. We show that an oscillating residual ansatz with spatial wavelength λ 0.1mm provides a better fit to the data compared to the residual Newtonian constant ansatz by ∆χ 2 = −15. Similar improved fits however, also occur in about 10% of Monte Carlo realization of Newtonian data on similar or larger scales. Thus, the significance level of this improved fit is at a level of not more than 2σ. The energy scale corresponding to this best fit wavelength is identical to the dark energy length scale λ de ≡ 4 c/ρ de ≈ 0.1mm.

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

“…Moreover, in classical point of view and in the case of doing an enough precise measurements, studying the test particle's trajectory can tell us whether the deviation of acceleration is due to the intrinsic curvature of the universe or the extrinsic one which is induced by the constrained structure of the model. Also, one can obtain the estimate of relative radii of the torus, and in addition one can verify what the topology of the universe would be [85].…”

Newtonian potential and geodesic completeness in infinite derivative gravity

“…For D > 10, (27) is a very good approximation and so increasing the value of D does not change the potential. Our next task is to investigate the choice of large powers of k 2 which has been shown to fit recent experimental data [34] at small distances for the a( ) = c( ) case. We will see whether we can still obtain oscillating solutions with conditions necessary to realise defocusing.…”

“…For illustrative purposes, we have taken M p = 1m −1 . We can parameterise these curves as α 1 r for r < 1 and α 2 cos(θr + θ 0 )/r for r > 1, where α 1 , α 2 , θ and θ 0 are constants, as in [34].…”

“…If we generalise this further by taking a( ) to be an exponential of a higher order polynomial, the potential is modified by an oscillating function at these higher orders. Analysis by Perivolaropoulos [2,34] has shown that this oscillating function provides a better fit to experimental data on the force of gravity at small distances than the standard GR theory. Although further analysis is needed, there are tantalising hints that modified gravity could provide the correct description of the strength of gravity at small distances.…”

Quantum spreading of a self-gravitating wave-packet in singularity free gravity

“…The current constraints on M s comes from torsion-balance experiments which have seen no departure from the Newtonian 1/r -fall up to a distance of 5.6 × 10 −5 meters, that implies M s ≥ 0.004 eV [34,35].…”