We consider a quantum scalar field on an arbitrary gravitational background. We obtain the effective in-in equations for the gravitational fields using a covariant and non-local approximation for the effective action proposed by Vilkovisky and collaborators. From these equations, we compute the quantum corrections to the Newtonian potential. We find logarithmic corrections which we identify as ...

Progress is reported from an oscillating torsion-pendulum experiment searching for gravitational inverse square law violation (ISLV) between macroscopic bodies with a separation of order 10 cm. An important design feature is the special mass configurations of both the pendulum and gravitational source. These provide high sensitivity to the horizontal derivative of the Laplacian of the gravitati...

The equations for the second-order gravitational perturbations produced by a compact-object have highly singular source terms at the point particle limit. At this limit the standard retarded solutions to these equations are ill-defined. Here we construct well-defined and physically meaningful solutions to these equations. These solutions are important for practical calculations: the planned gra...