The theory of general relativity has an ultraviolet(UV) problem that can be ameliorated by gravity with higher derivatives. The four-derivative gravity as an effective gravitational theory at UV scalars has two Yukawa-like corrections with parameters ${\lambda }_0$ and ${\lambda }_2$. By the analysis of experiments of HUST-2015, Newman’s group, lake experiment, and Cassini spacecraft, we obtain the strong-bound regions for these parameters at submillimeter-to-millimeter, centimeter-to-meter, tens-of-meter, and solar-system scales, in which the properties of potential are clearly shown. Recently, the ghostfree and singularityfree gravity, a more potential modified gravity theory, introduces the novel conception of nonlocality. We test the scale of gravitational nonlocality ${\lambda }_{\mathrm{m}}<2.7\times {10}^{-5}\mathrm{m}$ by the torsion pendulum experiment HUST-2015. The predicted decaying spatial oscillations are visible meaning possible violation at shorter ranges. Our result provides useful information for gravitational interaction at microscopic ranges.

• Received 11 January 2019

DOI:https://doi.org/10.1103/PhysRevD.99.104008