We evaluate the modifications to the cosmic microwave background anisotropy spectrum that result from a semiclassical expansion of the Wheeler-DeWitt equation. Recently, such an investigation in the case of a real scalar field coupled to gravity has led to the prediction that the power at large scales is suppressed. We make here a more general analysis and show that there is an ambiguity in the choice of solution to the equations describing the quantum gravitational effects. Whereas one of the two solutions describes a suppression of power, the other one describes an enhancement.

We complete the analytical determination, at the 4th post-Newtonian approximation, of the main radial potential describing (within the effective one-body formalism) the gravitational interaction of two bodies. The (non logarithmic) coefficient $a_5(\nu)$ measuring this 4th post-Newtonian interaction potential is found to be linear in the symmetric mass ratio $\nu$. Its $\nu$-independent part $a_5(0)$ is obtained by an analytical gravitational self-force calculation that unambiguously resolves the formal infrared divergencies which currently impede its direct post-Newtonian calculation.