Possible violation of Newtonian gravitational law at small distances and   constraints on it from the Casimir effect
  The recent ideas that the gravitational and gauge interactions become united at the weak scale lead to Yukawa-type corrections to the Newtonian gravitational law at small distances. We briefly summarize the best constraints on these corrections obtained recently from the experiments on the measurement of the Casimir force. The new constraints on the Yukawa-type interaction are derived from the latest Casimir force measurement between a large gold coated sphere and flat disk using an atomic force microscope. The obtained constraints are stronger up to 19 times comparing the previous experiment with aluminum surfaces and up to 4500 times comparing the Casimir force measurements between dielectrics. The application range of constraints obtained by means of an atomic force microscope is extended. 
V.M.Mostepanenko, M.Novello