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

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