Quantum loop effects during inflation and a possible connection to nonlocal gravity

The inflation scenario tells us that quantum fluctuations are vastly amplified during inflation and seed the large scale structure of the universe. As an example of quantifying some quantum effects during inflation, I have considered the graviton field interacting with the quantum scalar field in de Sitter background which modifies (or quantum corrects) the linearized Einstein equations. Solving the quantum corrected Einstein equations for a static point mass leads to corrections to the Newtonian potential, which corresponds to a time-varying Newton’s constant. On the other hand, a class of nonlocal gravity models which adds some nonlocal corrections to the Einstein equations has been devised to simulate the late-time cosmic acceleration. Though a derivation of the model from first principles is not available yet, there is some implication that those nonlocal terms might be originated from quantum corrections during inflation. I will discuss what is the connection between quantum corrections during inflation and nonlocal gravity, as well as open problems regarding this possibility.