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

TL;DR

It is found with 95% confidence that the inverse-square law holds (|alpha| <or=1) down to a length scale lambda=56 microm and that an extra dimension must have a size R<or=44 microm.

Abstract

We conducted three torsion-balance experiments to test the gravitational inverse-square law at separations between 9.53 mm and 55 micrometers, probing distances less than the dark-energy length scale $λ_{\rm d}=\sqrt[4]{\hbar c/ρ_{\rm d}}\approx 85 μ$m. We find with 95% confidence that the inverse-square law holds ($|α| \leq 1$) down to a length scale $λ= 56 μ$m and that an extra dimension must have a size $R \leq 44 μ$m.

Figures (6)

• Figure 1: Scale drawing of our detector and attractor. The 3 small spheres near the top of the detector were used for a continuous gravitational calibration of the torque scale. Four rectangular plane mirrors below the spheres are part of the twist-monitoring system. The detector's electrical shield is not shown.
• Figure 2: Fourier transform of the raw twist signal in Experiment III taken at $s=67~\mu$m (a detector-membrane separation of 46 $\mu$m). The detector's free resonance occurs at 7.5$\omega$ and the gravitational calibration is at 9$\omega$. The peaks at 21, 42 and 63$\omega$ probe the inverse square law. The smooth curve shows the thermal noise level. At this small separation the torque noise power retains the expected $1/f$ form, but its amplitude exceeds the thermal value by about a factor of four.
• Figure 3: [Color online] Experiment I torques as functions of vertical separation $s$. The horizontal scale is expanded below $s=100~\mu$m. The upper panel displays the 21$\omega$ and 42$\omega$ torques as solid circles and squares, respectively. When not visible the errors are smaller than the size of the points. The smooth curves show the Newtonian fit to the combined data of all 3 experiments. The lower panel shows the 21$\omega$ residuals; the smooth curve shows the residual that would arise from an $\alpha =1$, $\lambda = 80~\mu$m Yukawa interaction.
• Figure 4: [Color online] Experiment II torques. Notation is the the same as for Fig. \ref{['fig: data exp 1']}, but the vertical scales are expanded.
• Figure 5: [Color online] Experiment III torques. Notation is the same as in Fig. \ref{['fig: data exp 2']}, except that diamonds (triangles) show the 21$\omega$ torque from the upper (lower) attractor plate alone. The solid and dashed curves in the lower panel show the residuals expected from $\alpha=1$, $\lambda=80~\mu$m and $\alpha=10^5$, $\lambda=10~\mu$m Yukawa interactions, respectively. Both are excluded by our results.