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 like the Planck mass and the effective Brans--Dicke parameter, $\omega$. In the particular case of Brans--Dicke gravity, where $\omega$ is constant, this leads to runaway solutions with infinitely large values of the Planck mass. However, in a theory with variable $\omega$ we find stationary probability distributions with a finite value of the Planck mass peaked at exponentially large values of $\omega$ after inflation. We conclude that general relativity is an attractor during the quantum diffusion of the fields.