General relativity as an attractor in scalar-tensor stochastic inflation

Quantum fluctuations of scalar fields during inflation could determine the very-large-scale structure of the universe In the case of general scalar-tensor gravity theories these fluctuations lead to the diffusion of fundamental constants such as the Planck mass and the effective Brans-Dicke parameter {ω}. In the particular case of Brans-Dicke gravity, where {ω} is constant, this leads to runaway solutions with infinitely large values of the Planck mass. However, in a variable {ω} theory, if the Planck mass has a maximum, we find stationary probability distributions peaked at exponentially large values of {ω} after inflation. We conclude that general relativity is an attractor during the quantum diffusion of the fields.