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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, $ω$. 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 theory with variable $ω$ we find stationary probability distributions with a finite value of the Planck mass peaked at exponentially large values of $ω$ after inflation. We conclude that general relativity is an attractor during the quantum diffusion of the fields.